Advertisements
Advertisements
Question
Prove the following identity :
`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`
Advertisements
Solution
LHS = `(secA - 1)/(secA + 1) = (1/cosA - 1)/(1/cosA + 1)`
= `(1 -cosA)/(1 + cosA) = "RHS"`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(tan A + tan B)/(cot A + cot B) = tan A tan B`
Prove the following identities:
`cosecA + cotA = 1/(cosecA - cotA)`
Prove the following identities:
`(cosecA - 1)/(cosecA + 1) = (cosA/(1 + sinA))^2`
Prove that:
(sin A + cos A) (sec A + cosec A) = 2 + sec A cosec A
Show that none of the following is an identity:
(i) `cos^2theta + cos theta =1`
If sec θ + tan θ = x, then sec θ =
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identity :
`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`
To prove cot θ + tan θ = cosec θ × sec θ, complete the activity given below.
Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
If sin A = `1/2`, then the value of sec A is ______.
