Advertisements
Advertisements
Question
Write the value of`(tan^2 theta - sec^2 theta)/(cot^2 theta - cosec^2 theta)`
Solution
`(tan^2 theta - sec^2 theta )/ (cot^2 theta - cosec^2 theta)`
=` (-1)/(-1)`
= 1
APPEARS IN
RELATED QUESTIONS
Prove that sin6θ + cos6θ = 1 – 3 sin2θ. cos2θ.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x2 + y2 + z2 = r2
`1+(tan^2 theta)/((1+ sec theta))= sec theta`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
What is the value of \[6 \tan^2 \theta - \frac{6}{\cos^2 \theta}\]
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Prove the following identity :
`sqrt(cosec^2q - 1) = "cosq cosecq"`
There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are 30° and 60° respectively. Find the width of the river and height of the other pole.
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that `sqrt((1 + sin θ)/(1 - sin θ))` = sec θ + tan θ.
Prove that cos θ sin (90° - θ) + sin θ cos (90° - θ) = 1.
If x = a tan θ and y = b sec θ then
Choose the correct alternative:
sin θ = `1/2`, then θ = ?
Prove that `(1 + sec "A")/"sec A" = (sin^2"A")/(1 - cos"A")`
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
Factorize: sin3θ + cos3θ
Hence, prove the following identity:
`(sin^3θ + cos^3θ)/(sin θ + cos θ) + sin θ cos θ = 1`
