Trigonometry MCQs

Question 1

If tan40° = α, then find $$\frac{{	an {{320}^ \circ } - 	an {{310}^ \circ }}}{{1 + 	an {{320}^ \circ } \cdot 	an {{310}^ \circ }}}$$

Accepted Answer

$$\frac{{1 - {\alpha ^2}}}{{2\alpha }}$$

Answer

$$\frac{{1 - {\alpha ^2}}}{\alpha }$$

Answer

$$\frac{{1 + {\alpha ^2}}}{{2\alpha }}$$

Answer

$$\frac{{1 + {\alpha ^2}}}{\alpha }$$

Question 2

$$\frac{{\sin 	heta - \cos 	heta + 1}}{{\sin 	heta + \cos 	heta - 1}} = ?$$

Accepted Answer

secθ + tanθ

Answer

secθsinθ

Answer

secθtanθ

Answer

secθ - tanθ

Question 3

If $${	ext{2cos}}	heta - \sin 	heta = \frac{1}{{\sqrt 2 }},$$ $$\left( {{0^ \circ } < 	heta < {{90}^ \circ }} ight)$$ the value of $$2\sin 	heta $$ + $$\cos 	heta $$ is?

Accepted Answer

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

Answer

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

Answer

$$\sqrt 2 $$

Answer

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

Question 4

If $$x = \frac{{2\sin 	heta }}{{1 + \cos 	heta + \sin 	heta }},$$ then the value of $$\frac{{1 - \cos 	heta + \sin 	heta }}{{1 + \sin 	heta }}$$ is

Accepted Answer

$$x$$

Answer

$$\frac{x}{{1 + x}}$$

Answer

$$\frac{1}{x}$$

Answer

$$\frac{{1 + x}}{x}$$

Question 5

If θ is a positive acute angle and 4cos 2 θ - 1 = 0, then the value of tan(θ - 15°) is equal to?

Accepted Answer

1

Answer

0

Answer

$$\sqrt 3 $$

Answer

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

Question 6

If sinθ × cosθ = $$\frac{1}{2}{	ext{,}}$$ Then the value of sinθ - cosθ is where 0° < θ < 90°.

Accepted Answer

0

Answer

$$\sqrt 2 $$

Answer

2

Answer

1

Question 7

If sin(A + B) = cos(A + B), what is the value of tanA?

Accepted Answer

$$\frac{{1 - 	an B}}{{1 + 	an B}}$$

Answer

$$\frac{{1 + 	an B}}{{1 - 	an B}}$$

Answer

$$\frac{{1 + \sec B}}{{1 - \sec B}}$$

Answer

$$\frac{{1 - {	ext{cosec}}\,B}}{{1 + {	ext{cosec}}\,B}}$$

Question 8

If P + Q + R = 60°, then what is the value of cosQcosR(cosP - sinP) + sinQsinR(sinP - cosP)?

Accepted Answer

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

Answer

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

Answer

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

Answer

$${\sqrt 2 }$$

Question 9

If the sum and difference of two angles are 135° and $$\frac{\pi }{{12}}$$ respectively, then the value of the angles in degree measure are?

Accepted Answer

75°, 60°

Answer

70°, 65°

Answer

45°, 90°

Answer

80°, 55°