Bissoy.com
Doctors Medicines MCQs Q&A

Barack Obama, the 44th US. president is always confused in trigonometry Donald Trump give him a question in which cosecθ - sinθ = x3 and secθ - cosθ = y3. Then, find the value of x2y2(x2 + y2) for him. 

Barack Obama, the 44th US. president is always confused in trigonometry Donald Trump give him a question in which cosecθ - sinθ = x3 and secθ - cosθ = y3. Then, find the value of x2y2(x2 + y2) for him.  Correct Answer 1

Given∶

cosec

θ - sin

θ = x3 and sec

θ - cos

θ = y3

Formula Used∶

 

Basics of Trigonometry.

sin2θ + cos2θ = 1

Calculation∶

cosec

θ - sin

θ = x3

⇒ 1/sin

θ - sin

θ = x3

⇒ (1 - sin2θ ) / sinθ = x3

⇒ cos2θ /sinθ = x3

⇒ x = (cos2θ /sinθ )1/3      ---(1)

Also, secθ - cosθ = y3

⇒ 1/cosθ - cosθ = y3

⇒ (1 - cos2θ )/cosθ = y3

⇒ sin2θ /cosθ = y3

⇒ sin2θ /cosθ = y3

⇒ y = (sin2θ /cosθ )1/3      ---(2)

Now take,

⇒ (cos2θ /sinθ)2/3(sinθ/cosθ)2/3     

⇒ (cos2θ.sin2θ/sinθ.cosθ]2/3

⇒ (cosθ.sinθ)2/3

⇒ (cosθ.sinθ)2/3[(cos2θ / sinθ)2/3+ (cosθ.sinθ)2/3(sin2θ /cosθ )2/3

⇒ (cosθ.sinθ.cos2θ/sinθ)2/3+ (cosθ.sinθ.sin2θ/cosθ)2/3

⇒ (cos3θ)2/3 + (sin3θ)2/3

⇒ cos2θ + sin2θ

⇒ 1

∴ The correct option is 4.

Related Questions

Statement: US President Donald Trump on Thursday cancelled the talks scheduled for June 12 with North Korean leader Kim Jong-un. Which of the following objection(s) might be a probable reason(s) for the above-taken step by US President Donald Trump? I. The US President cited North Korea's recent "tremendous anger and open hostility" as the reason for him cancelling the summit. II. Donald Trump did not want to make any relations with North Korea and wants a nuclear war between the two nations and as a result has cancelled the summit. III. In a letter to the North Korean Leader, US president cited that the statements released by the North Korean Vice Minister Choe Son-hui represented "tremendous anger and open hostility", as a reason for cancelling the summit. IV. North Korea is the US’s rival and building any relationship with the Korean nation will bring economic harm to the US and as a result has cancelled the summit.
A statement is given followed by two inferences I and II. You have to consider the statement to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given inferences, if any, follow from the given statement? Statement: U.S. President Donald Trump signed an order on Tuesday to keep open the military detention centre at Guantanamo Bay after his Democratic predecessor, Barack Obama, tried unsuccessfully to close the prison that has drawn international condemnation. Inferences: Guantanamo Bay Detention Centre was never closed during the reign of President Barack Obama. Guantanamo Bay Detention Centre would increase the capacity to accommodate detainees.
If \(\frac{(1 +sinθ-cosθ)}{(1 +sinθ +cosθ)} + \frac{(1 + sinθ +cosθ)}{(1 + sinθ-cosθ)}\)= 4, then which of the following values will be suitable for θ ?
In the question given below, the sentence is divided into three parts I, II, III. For each part, an alternate statement is also given. You have to determine if a part requires correction, and then mark that as your answer. The U.S. was offering support to Saudi Arabia’s campaign/ against the Houthi rebels in Yemen/ when Barack Obama is the president. I. The U.S. offered support to Saudi Arabia’s campaign II. against a Houthi rebels in Yemen III. when Barack Obama was the president.
The statements given below are followed by two conclusions labeled I and II. Assuming that the information in the statement is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements. Statements: All Obama are Trump. Some Trump are Clinton. Conclusions: I. Some Obama are Clinton. II. All Clinton are Trump.
If (secθ + cosecθ)/(secθ - cosecθ) = 7 then what will be the value of secθ?
The question given below consists of a statement, followed by three arguments numbered I, II and III. You have to decide which of the arguments is/are ‘strong' arguments and which is/are ‘weak' arguments and accordingly choose your answer from the alternatives given below each question. Statement: The United States has launched what China calls the ‘largest trade war in economic history' and in its latest move targeted another $200 billion in Chinese export goods. The US-China spat is one of several trade fights picked by the protectionist President Donald Trump as his ‘America First' agenda disrupts trade relations among traditional allies. The growing share of international trade under threat has raised the prospect the escalating trade war could harm the global economy, shrinking investments and undermining supply chains. Why? Arguments: I. Several companies - including Total and Peugeot of France, and Russia's Lukoil - have said they are preparing to exit Iran ahead of US deadlines, the last of which is November 4. II. Trump argued the original deal from 2012 was lopsided in Seoul's favour but has also clouded the issue by appearing to link trade concessions to progress in his separate track of talks with nuclear-armed North Korea. III. Meanwhile, talks among the three NAFTA (North American Free Trade Agreement) signatories, launched after Trump demanded an overhaul of the ‘terrible deal', have snagged notably owing to the US demands to increase American content installed in duty-free autos. 
In the US, the Pentagon is cancelling the construction of parts of former US President Donald Trump’s border wall with Mexico. Donald Trump had declared a national emergency in which year?
If (cosθ + sinθ) : (cosθ–sinθ) = (√3 + 1) : (√3 – 1),0° < θ 90°, then what is the value of secθ?
If secθ(cosθ + sinθ) = √2, then what is the value of 2sinθ/(cosθ - sinθ)?