Bissoy.com
Doctors Medicines MCQs Q&A

If sinθ + tanθ = 3√3/2, then what is the value of 5cosθ - 2sin2θ + 4tan2θ?

If sinθ + tanθ = 3√3/2, then what is the value of 5cosθ - 2sin2θ + 4tan2θ? Correct Answer 13

sinθ + tanθ = 3√3/2

sinθ + (sinθ/cosθ) = (√3 + 2√3)/2

sinθ + (sinθ/cosθ) = (√3/2) + √3

sinθ + (sinθ/cosθ) = (√3/2) +

After comparing:

sinθ = √3/2

cosθ = 1/2

tanθ = √3

Now,

= 5cosθ - 2sin2θ + 4tan2θ

= 5 × (1/2) - 2 × (√3/2)2 + 4 × (√3)2

= (5/2) - (3/2) + 12

= 13

Related Questions

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 ?
If 2 − cos2θ = 3 sinθ cosθ, where sinθ ≠ cosθ, the value of tanθ is.
যদি tanθ=512 এবং  cosθ  ধনাত্মক হয় , তবে sinθ+cos(-θ)sec(-θ)+tanθ এর মান হবে -
tanθ=512 এবং cosθ ঋণাত্মক হলে, sinθ+cos(-θ)sec(-θ)+tanθ=?
tanθ=−512 এবং tanθ, sinθ একই চিহ্নযুক্ত হলে,sec θ এর মান কত?
The expression (tanθ + cotθ)(secθ + tanθ)(1 - sinθ), 0°
যদি tanθ=ab  হয়, তবে a sinθ-b cosθa sinθ+b cosθ এর মান হবে-
θ is being an acute angle, it is given that sec2θ + 4tan2θ = 6. What is the value of θ?
tanθ + secθ = x হলে, cosecθ-এর মান কত? (If tanθ + secθ = x, then what is the value of cosecθ)
If 5 secθ – 3 tanθ = 5, then what is the value of 5 tanθ – 3 secθ?