Complementary Trigonometric Ratios

Q.

Find the value of $\tan 1^{\circ }\tan 2^{\circ }\tan 3^{\circ }.......\tan {89}^{\circ }$.

Q.

If sin$\theta$ = cos$\theta$, then value of $\theta$ is

1. 45 degrees

2. 30 degrees

3. 90 degrees

4. 0 degrees

Q.

If $7si{n}^2\theta +3co{s}^2\theta =4$, then $sec\theta +cosec\theta$ is equal to

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

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

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

4. None of these

Q. If tan2A = cot(A-${18}^{\circ }$), then value of A (in degrees) is:

1. 36

Q. The value of $co{s}^2{5}^{\circ }+co{s}^2{10}^{\circ }+co{s}^2{15}^{\circ }+\dots \dots \dots ..+co{s}^2{85}^{\circ }+co{s}^2{90}^{\circ }$ is equal to

1. 10
2. 9/2
3. 17/2
4. 19/2

Q.

Prove that (cosecA-sinA)(secA-cosA)=1/tanA+cotA

Q.

Write all the other trigonometric ratios of $\angle A$ in terms of $\text{sec}A.$

Q. Question 4
If tan A = cot B, prove that $A+B={90}^{\circ }$.

Q. Cot(1358°)+tan(3608°)=?

Q. Prove the following trigonometric identities.

(1 − cos² A) cosec² A = 1

Q.

If A and B are acute angle such that sin A = cos B then (A + B) = ?

(a) ${45}^o$ (b) ${60}^o$ (c) ${90}^o$ (a) ${180}^o$

Q.

If $\cos A=\frac{7}{25}$, find $\tan A+\cot A$

Q. Prove that
tan10 tan15 tan75 tan80=1

Q. If tan A= tan B, then A+B is

Q.

$\frac{\left(1-\tan 2°cot62°\right)}{\left(\tan 152°-cot88°\right)}=$

1. $\sqrt{3}$

2. $-\sqrt{3}$

3. $\sqrt{2}–1$

4. $1–\sqrt{2}$

Q.

Find the value of tan35°tan40°tan45°tan50°tan55°

Q.

P-1:-tan1.tan2.tan3......tan87.tan88.tan89=1

Q. Evaluate :
$cosec{31}^{\circ }-sec{59}^{\circ }$

Q. Prove the following trigonometric identities.

$\frac{{\tan }^3\theta }{1+{\tan }^2\theta }+\frac{{\cot }^3\theta }{1+{\cot }^2\theta }=\sec \theta \mathrm{cosec}\theta -2\sin \theta \cos \theta$

Q.

Find the value of $\frac{4}{3}ta{n}^2{60}^{\circ }+3co{s}^2{30}^{\circ }-2se{c}^2{30}^{\circ }-\frac{3}{4}co{t}^2{60}^{\circ }$

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

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

3. 3

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

Q. Prove that
Sec41°sin49° + cos29°cosec61° - 2/√3(tan20°tan60°tan30°)/3(sin^31° + sin^59°)=0

Q. Let $f$ be an odd function defined on the real numbers such that $f\left(x\right)=3\sin x+4\cos x$, for $x\ge 0$, then $f\left(x\right)$ for $x<0$ is

1. $3\sin x-4\cos x$
2. $-3\sin x+4\cos x$
3. $-3\sin x-4\cos x$
4. $3\sin x+4\cos x$

Q. Question 2
If $sinA=\frac{1}{2}$, then the value of cot A is

(A) $\sqrt{3}$
(B) $\frac{1}{\sqrt{3}}$
(C) $\frac{\sqrt{3}}{2}$
(D) $1$

Q. tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to

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

Q.

All formula of trigonometry

Q. Find the value of sin 1020° + tan750°

Q.

What is the maximum value of $\sin$?

Q.

Find the value of (, tan1°tan4°tan6°........tan88°).

Q.

If sin theta= 21/29 then evaluate sec thetha/ tan theta - sin theta

Q. What is the value of $6{\tan }^2\theta -\frac{6}{{\cos }^2\theta }$.