Advertisements
Advertisements
Question
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
Advertisements
Solution
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
L.H.S. = `(1 - tan^2theta)/(cot^2 theta - 1)`
= `1 - tan^2theta ÷ 1/(tan^2theta) - 1`
= `1 - tan^2theta ÷ (1 - tan^2theta)/(tan^2theta)`
= `(1 - tan^2theta) xx (tan^2theta)/((1 - tan^2 theta))`
= tan2 θ
L.H.S. = R.H.S.
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
`(sin theta+1-cos theta)/(cos theta-1+sin theta) = (1+ sin theta)/(cos theta)`
Write the value of tan10° tan 20° tan 70° tan 80° .
If tanθ `= 3/4` then find the value of secθ.
Prove that secθ + tanθ =`(costheta)/(1-sintheta)`.
Prove the following identity :
sinθcotθ + sinθcosecθ = 1 + cosθ
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
Prove the following identities.
(sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2
If 2sin2β − cos2β = 2, then β is ______.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
