Consider the following (1) 2(Tan 30°Cot 30° + Tan 45° Cot 45°) = 4(Sin 90° + Cos 90°) (2) (Sin 30°+ 1)/(Cos 60° + 1) = Tan 45° (3) Tan 45° + Cot 45° = 2 Which of the above statement(s) is/are correct?

Evaluate the following:
$$\frac{{\cos 2\theta \cdot \cos 3\theta - \cos 2\theta \cdot \cos 7\theta + \cos \theta \cdot \cos 10\theta }}{{\sin 4\theta \cdot \sin 3\theta - \sin 2\theta \cdot \sin 5\theta + \sin 4\theta \cdot \sin 7\theta }}$$

A

cot6θ.cot5θ

B

cos6θ.cos5θ

C

cos6θ.cot5θ

D

-cot6θ.cot5θ

Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy. ]) b) (-x3 Cos(x) – 3x2 Sin(x) – 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3]) c) (-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y)) d) (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))

A

(x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(y3 Cos(y) + 3]) ) c) (-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y)) d) (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y)) View Answer]

B

y2 Sin(y) – 2[-yCos(y) + Sin(y)

C

y2 Sin(y) – 2[-yCos(y) + Sin(y)

D

y2 Sin(y) – 2[-yCos(y) + Sin(y)

The value of the expression:sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89° is?

A

0

B

$${\text{5}}\frac{1}{2}$$

C

$${\text{4}}\frac{1}{2}$$

D

5

What is the value of {[sin (x + y) – 2 sin x + sin (x – y)]/[cos (x – y) + cos (x + y) – 2 cos x]} × [(sin 10x – sin 8x)/(cos 10x + cos 8x)]?

A

0

B

tan2x

C

1

D

2 tan x

The value of $$\frac{{4{{\tan }^2}{{30}^ \circ } + {{\sin }^2}{{30}^ \circ }{{\cos }^2}{{45}^ \circ } + {{\sec }^2}{{48}^ \circ } - {{\cot }^2}{{42}^ \circ }}}{{\cos {{37}^ \circ }\sin {{53}^ \circ } + \sin {{37}^ \circ }\cos {{53}^ \circ } + \tan {{18}^ \circ }\tan {{72}^ \circ }}}\,{\text{is:}}$$

A

$$\frac{{49}}{{24}}$$

B

$$\frac{{35}}{{48}}$$

C

$$\frac{{35}}{{24}}$$

D

$$\frac{{59}}{{48}}$$

What is the value of $$\frac{{32{{\cos }^6}x - 48{{\cos }^4}x + 18{{\cos }^2}x - 1}}{{4\sin x\,\cos x\,\sin \left( {60 - x} \right)\cos \left( {60 - x} \right)\sin \left( {60 + x} \right)\cos \left( {60 + x} \right)}}?$$

A

4tan6x

B

4cot6x

C

8cot6x

D

8tan6x

If θ = 9°, then what is the value of Cot θ cot 2 θ cot 3 θ cot 4 θ cot 5 θ cot 6 θ cot 7 θ cot 8 θ cot 9 θ ?

A

13

B

3 - 1

C

1

D

3

Let the function
\[{\text{f}}\left( \theta \right) = \left| {\begin{array}{*{20}{c}} {\sin \theta }&{\cos \theta }&{\tan \theta } \\ {\sin \left( {\frac{\pi }{6}} \right)}&{\cos \left( {\frac{\pi }{6}} \right)}&{\tan \left( {\frac{\pi }{6}} \right)} \\ {\sin \left( {\frac{\pi }{3}} \right)}&{\cos \left( {\frac{\pi }{3}} \right)}&{\tan \left( {\frac{\pi }{3}} \right)} \end{array}} \right|\

A

where \\

B

and \ denote the derivative of f with respect to \. Which of the following statements is/are TRUE?
I. There exists \ such that \
II. There exists \ such that\

C

A. l only

D

ll only

If A + B = 90°, then which of the following is correct? A. sin A = cos B B. sin A + cos B = 0 C. sin A – cos B = 1 D. sin A – cos B = 2

A

C

B

A

C

B

D

The value of [sin (X + Y) cos (X + Y) + sin (X - Y) cos (X - Y)]/[sin (X + Y) cos (X - Y) + sin (X - Y) cos (X + Y)] is:

A

sin 2X

B

sin 3Y

C

cos 2X

D

cos 2Y

Consider the following (1) 2(Tan 30°Cot 30° + Tan 45° Cot 45°) = 4(Sin 90° + Cos 90°) (2) (Sin 30°+ 1)/(Cos 60° + 1) = Tan 45° (3) Tan 45° + Cot 45° = 2 Which of the above statement(s) is/are correct?

Related Questions