Advertisements
Advertisements
Question
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Advertisements
Solution
L.H.S. = `1/(1+cosA)+1/(1-cosA)`
= `(1 - cosA + 1 + cosA)/((1 + cosA)(1 - cosA))`
= `2/(1 - cos^2A)` ...(∵ 1 – cos2 A = sin2 A)
= `2/(sin^2A)`
= 2 cosec2 A = R.H.S.
APPEARS IN
RELATED QUESTIONS
`1/((1+tan^2 theta)) + 1/((1+ tan^2 theta))`
What is the value of (1 + tan2 θ) (1 − sin θ) (1 + sin θ)?
\[\frac{1 - \sin \theta}{\cos \theta}\] is equal to
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Prove that `(tan^2 theta - 1)/(tan^2 theta + 1)` = 1 – 2 cos2θ
cot θ . tan θ = ?
Which is not correct formula?
If 2 cos θ + sin θ = `1(θ ≠ π/2)`, then 7 cos θ + 6 sin θ is equal to ______.
sec θ when expressed in term of cot θ, is equal to ______.
(sec2 θ – 1) (cosec2 θ – 1) is equal to ______.
