Advertisements
Advertisements
Question
Prove the following identity :
`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`
Advertisements
Solution
LHS = `(cosecA - sinA)(secA - cosA)`
= `(1/sinA - sinA)(1/cosA - cosA)`
= `((1-sin^2A)/(sinA))((1 - cos^2A)/cosA)`
= `(cos^2A/sinA)(sin^2A/cosA)` = cosA.sinA
RHS = `1/(tanA + cotA)`
= `1/(sinA/cosA + cosA/sinA) = 1/((sin^2A + cos^2A)/(sinA.cosA))` = cosA.sinA
Hence , LHS = RHS
APPEARS IN
RELATED QUESTIONS
If 3 sin θ + 5 cos θ = 5, prove that 5 sin θ – 3 cos θ = ± 3.
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Show that none of the following is an identity:
`cos^2theta + cos theta = 1`
Write the value of `cosec^2 theta (1+ cos theta ) (1- cos theta).`
`If sin theta = cos( theta - 45° ),where theta " is acute, find the value of "theta` .
If `secθ = 25/7 ` then find tanθ.
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Prove the following identity :
`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`
If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `± sqrt(a^2 + b^2 - c^2)`
