Advertisements
Advertisements
Question
Prove that `sqrt((1 + cos A)/(1 - cos A)) = (tan A + sin A)/(tan A. sin A)`
Advertisements
Solution
LHS = `sqrt(((1 + cos A)(1 + cos A))/((1 - cos A)(1 + cos A)))`
= `sqrt((1 + cos A)^2/(1 - cos^2 A))`
= `sqrt((1 + cos^2 A + 2cos A)/sin^2 A`
= `(1 + cos A)/sin A`
RHS = `(tan A + sin A)/(tan A sin A)`
= `(sin A(1/cos A + 1))/((sin A/cos A xx sin A)`
= `(sin A( 1 + cos A))/cos A xx cos A/(sin A sin A)`
= `(1 + cos A)/sin A`
Hence proved.
RELATED QUESTIONS
Prove the following trigonometric identities.
(cosec θ − sec θ) (cot θ − tan θ) = (cosec θ + sec θ) ( sec θ cosec θ − 2)
If `cos theta = 7/25 , "write the value of" ( tan theta + cot theta).`
Simplify : 2 sin30 + 3 tan45.
What is the value of \[\sin^2 \theta + \frac{1}{1 + \tan^2 \theta}\]
What is the value of \[\frac{\tan^2 \theta - \sec^2 \theta}{\cot^2 \theta - {cosec}^2 \theta}\]
cos4 A − sin4 A is equal to ______.
Prove that `sqrt((1 + sin A)/(1 - sin A))` = sec A + tan A.
Prove that `( 1 + sin θ)/(1 - sin θ) = 1 + 2 tan θ/cos θ + 2 tan^2 θ` .
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If tan θ = `x/y`, then cos θ is equal to ______.
