Advertisements
Advertisements
Question
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Advertisements
Solution
LHS = `cos^4A - sin^4A`
= `(cos^2A - sin^2A)(cos^2A + sin^2A)`
= `{cos^2A - (1 - cos^2A)} = 2cos^2A - 1` = RHS
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A + 1) = 1`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
If sec A + tan A = p, show that:
`sin A = (p^2 - 1)/(p^2 + 1)`
If (tan θ + sin θ) = m and (tan θ – sin θ) = n, prove that (m2 – n2)2 = 16 mn.
The value of (1 + cot θ − cosec θ) (1 + tan θ + sec θ) is
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
Prove the following identity :
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that: sin4 θ + cos4θ = 1 - 2sin2θ cos2 θ.
