Trigonometry MCQs

Question 1

The value of $$1 + \sqrt {\frac{{\cot 	heta + \cos 	heta }}{{\cot 	heta - \cos 	heta }}} ,$$ if 0° < θ < 90°, is equal to:

Accepted Answer

1 + secθ + tanθ

Answer

1 - secθ + tanθ

Answer

1 - secθ - tanθ

Answer

1 + secθ - tanθ

Question 2

If A = sin 2 θ + cos 4 θ for any value of θ, then the value of A is?

Accepted Answer

$$\frac{3}{4} \leqslant {	ext{A}} \leqslant {	ext{1}}$$

Answer

$${	ext{1}} \leqslant {	ext{A}} \leqslant {	ext{1}}$$

Answer

$$\frac{{13}}{{16}} \leqslant {	ext{A}} \leqslant {	ext{1}}$$

Answer

$$\frac{3}{4} \leqslant {	ext{A}} \leqslant \frac{{13}}{{16}}$$

Question 3

If sinθ = 4cosθ, then what is the value of sinθcosθ?

Accepted Answer

$$\frac{4}{{17}}$$

Answer

$$\frac{2}{9}$$

Answer

$$\frac{3}{{10}}$$

Answer

$$\frac{3}{4}$$

Question 4

If 3(cot 2 θ - cos 2 θ) = cos 2 θ, 0°< θ < 90°, then the value of (tan 2 θ + cosec 2 θ + sin 2 θ) is:

Accepted Answer

$$\frac{{61}}{{12}}$$

Answer

$$\frac{{13}}{3}$$

Answer

$$\frac{{25}}{{12}}$$

Answer

$$\frac{{15}}{4}$$

Question 5

If 4 - 2sin 2 θ - 5cosθ = 0, 0° < θ < 90°, then the value of sinθ + tanθ is:

Accepted Answer

$$\frac{{3\sqrt 3 }}{2}$$

Answer

$$\frac{{3\sqrt 2 }}{2}$$

Answer

$$3\sqrt 2 $$

Answer

$$2\sqrt 3 $$

Question 6

If $$\sqrt 3 $$ tanθ = 3sinθ, then the value of (sin 2 θ - cos 2 θ) is?

Accepted Answer

$$\frac{1}{3}$$

Answer

1

Answer

3

Answer

None of these

Question 7

If cosθ + sinθ = $$\sqrt 2 $$ cosθ, then cosθ - sinθ is?

Accepted Answer

$$\sqrt 2 $$ sinθ

Answer

$$\sqrt 2 $$ tanθ

Answer

-$$\sqrt 2 $$ cosθ

Answer

-$$\sqrt 2 $$ sinθ

Question 8

If $${	ext{sin}}\left( {{{90}^ \circ } - 	heta } ight)$$ + $${	ext{cos}}	heta $$ = $$\sqrt 2 {	ext{cos}}\left( {{{90}^ \circ } - 	heta } ight){	ext{,}}$$ then the value of $${	ext{cosec}}	heta $$ is?

Accepted Answer

$$\sqrt {\frac{3}{2}} $$

Answer

$$\frac{1}{{\sqrt 3 }}$$

Answer

$$\frac{2}{3}$$

Answer

$$\frac{1}{{\sqrt 2 }}$$

Question 9

If $${	ext{tan }}{9^ \circ } = \frac{p}{q}{	ext{,}}$$ then the value of $$\frac{{{	ext{se}}{{	ext{c}}^2}{	ext{8}}{{	ext{1}}^ \circ }}}{{1 + {{\cot }^2}{{81}^ \circ }}}$$ is?

Accepted Answer

$$\frac{{{q^2}}}{{{p^2}}}$$

Answer

$$\frac{p}{q}$$

Answer

1

Answer

$$\frac{{{p^2}}}{{{q^2}}}$$