Value of Standard Angle(30,60,90)

Q. The value of $4co{t}^2{45}^{\circ }-se{c}^2{60}^{\circ }+si{n}^2{60}^{\circ }+co{s}^2{90}^{\circ }$ is

1. $\frac{1}{2}$
2. $\frac{3}{4}$
3. $\frac{5}{2}$
4. $0$

Q.

If x = a cos θ and y = b sin θ then b²x² + a²y² is equal to

1. ab

2. a² + b²

3. a²b²

4. a⁴b⁴

Q.

The value of $\tan 30°\tan 60°$ is

Q. If θ is an acute angle such that sec² θ = 3, then the value of $\frac{{\tan }^2\theta -{\mathrm{cosec}}^2\theta }{{\tan }^2\theta +{\mathrm{cosec}}^2\theta }$is

(a) $\frac{4}{7}$
(b) $\frac{3}{7}$
(c) $\frac{2}{7}$
(d) $\frac{1}{7}$

Q. $\mathrm{Find}\mathrm{the}\mathrm{value}\mathrm{of}\frac{\cos 38°\mathrm{cosec}52°}{\tan 18°\tan 35°\tan 60°\tan 72°\tan 55°}.$

Q. If 5x = sec θ and $\frac{5}{x}=\tan \theta$, find the value of $5\left(x^2-\frac{1}{x^2}\right)$.

Q. The exact value of cosec 10°+ cosec 50° - cosec 70° is__________

Q. $$\begin{gathered} \mathrm{Choose}\mathrm{the}\mathrm{correct}\mathrm{answer}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{question}: \\ \frac{\sec 30°}{\mathrm{cosec}60°}=? \\ \left(\mathrm{a}\right)\frac{2}{\sqrt{3}}\left(\mathrm{b}\right)\frac{\sqrt{3}}{2}\left(\mathrm{c}\right)\sqrt{3}\left(\mathrm{d}\right)1 \end{gathered}$$

Q.

If sec θ = ¹³/₅ then tan θ is

1. 

2. 

3. 

4. 

Q. $\frac{cos{70}^{\circ }}{sin{20}^{\circ }}+\frac{cos{59}^{\circ }}{sin{31}^{\circ }}-8si{n}^2{30}^{\circ }$ is equal to

1. 0

Q. Find the principal value of cosec x=-1

Q. Find the value of $\frac{\text{Cot}{30}^{\circ }+\text{Cosec}{30}^{\circ }}{\text{Cot}{60}^{\circ }-\text{Cosec}{60}^{\circ }}$

1. $9\sqrt{3}+2$
2. $4\sqrt{3}-2$
3. $7\sqrt{3}-12$
4. $-3-2\sqrt{3}$

Q. Without using trigonometric tables, evaluate the following:

$\frac{\sec 37°}{\mathrm{cosec}53°}+2\cot 15°\cot 25°\cot 45°\cot 75°\cot 65°-3\left({\sin }^{2}18°+{\sin }^{2}72°\right)$

Q. In an equilateral triangle, a perpendicular drawn from one of the vertices to the opposite side as shown.The value of $Sin\theta$ is equal to

1. $\frac{1}{\sqrt{3}}$
2. $\frac{1}{\sqrt{2}}$
3. $\frac{1}{3}$
4. $\frac{1}{2}$

Q. If sec θ + tan θ = p, prove that sin θ = $\frac{p^2-1}{p^2+1}$

Q. If θ is an acute angle such that ${\tan }^2\theta =\frac{8}{7}$, then the value of $\frac{\left(1+\sin \theta \right)\left(1-\sin \theta \right)}{\left(1+\cos \theta \right)\left(1-\cos \theta \right)}$is

(a) $\frac{7}{8}$
(b) $\frac{8}{7}$
(c) $\frac{7}{4}$
(d) $\frac{64}{49}$

Q. Evaluate :- cosec 31degree - sec 59 degree

Q. If x = a cos θ and y = b sin θ, then b²x² + a²y² =

(a) a² b²
(b) ab
(c) a⁴ b⁴
(d) a² + b²

Q. Write the acute angle θ satisfying $\sqrt{3}\sin \theta =\cos \theta$.

Q. $\frac{sin{18}^{\circ }}{cos{72}^{\circ }}=$

Q.

If sec4A = cosec (A – 20^o), where 4A is an acute angle.

Find the value of A.

1. 82^o

2. 12^o

3. 62^o

4. 22^o

Q. What is the value of (1 + cot² θ) sin² θ?

Q. What is the value of Cosec W, if W = 90 degrees?

1. undefined
2. 1
3. 2
4. 0

Q. If sin θ = cos (θ − 45°), where θ and θ − 45° are acute angles, find the degree measure of θ.

Q.

If θ is an acute angle and, tanθ + cotθ = 2 then the value of tan⁷θ + cot⁷θ is

1. 2

2. 3

3. 6

4. 4

Q. Find the value of
$cose{c}^2{30}^{\circ }si{n}^2{45}^{\circ }-se{c}^2{60}^{\circ }.$

1. 1
2. 2
3. -2
4. 0

Q. If (cos θ + sec θ) = $\frac{5}{2}$, then (cos² θ + sec² θ) = ?
(a) $\frac{21}{4}$
(b) $\frac{17}{4}$
(c) $\frac{29}{4}$
(d) $\frac{33}{4}$

Q. $\mathrm{If}\sqrt{3}\sin \theta =\cos \theta \mathrm{and}\theta \mathrm{is}\mathrm{an}\mathrm{acute}\mathrm{angle},\mathrm{then}\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}\theta .$

Q. If sin 3 θ = cos (θ − 6°), where 3 θ and θ − 6° are acute angles, find the value of θ.

Q. If 2 cos θ − sin θ = x and cos θ − 3 sin θ = y. Prove that 2x² + y² − 2xy = 5.