Advertisements
Advertisements
Question
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Advertisements
Solution
LHS = `(cotA - cosecA)^2`
= `[cosA/sinA - 1/sinA]^2`
= `[(cosA - 1)/sinA]^2`
= `(cosA - 1)^2/sin^2A = (cosA - 1)^2/(1 - cos^2A)`
= `(-(1 - cosA))^2/((1 - cosA)(1 + cosA)) = ((1 - cosA)(1 - cosA))/((1 - cosA)(1 + cosA))`
= `(1 - cosA)/(1 + cosA)`
APPEARS IN
RELATED QUESTIONS
`(1+tan^2A)/(1+cot^2A)` = ______.
if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`
Prove the following trigonometric identities.
`tan theta + 1/tan theta` = sec θ.cosec θ
Prove the following trigonometric identities.
`cos theta/(1 + sin theta) = (1 - sin theta)/cos theta`
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Prove the following identities:
`(costhetacottheta)/(1 + sintheta) = cosectheta - 1`
If 2 sin A – 1 = 0, show that: sin 3A = 3 sin A – 4 sin3 A
Write True' or False' and justify your answer the following:
\[ \cos \theta = \frac{a^2 + b^2}{2ab}\]where a and b are two distinct numbers such that ab > 0.
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Prove that `(sin θ. cos (90° - θ) cos θ)/sin( 90° - θ) + (cos θ sin (90° - θ) sin θ)/(cos(90° - θ)) = 1`.
