Advertisements
Advertisements
Question
Prove the following trigonometric identities.
if cos A + cos2 A = 1, prove that sin2 A + sin4 A = 1
Advertisements
Solution
Given : `cos A + cos^2 A = 1`
we have to prove `sin^2 A + sin^4 A = 1`
Now
`cos A + cos^2 A = 1`
`=>cos A = 1 - cos^2 A`
`=> cos A = sin^2 A`
`=> sin^2 A = cos A`
Therefore, we have
`sin^2 A + sin^4 A = cos A + (cos A)^2`
`= cos A + cos^`2 A`
= 1
Hence proved.
APPEARS IN
RELATED QUESTIONS
If m=(acosθ + bsinθ) and n=(asinθ – bcosθ) prove that m2+n2=a2+b2
(secA + tanA) (1 − sinA) = ______.
Prove the following trigonometric identities.
`cosec theta sqrt(1 - cos^2 theta) = 1`
Prove the following identities:
`1 - sin^2A/(1 + cosA) = cosA`
`tan theta/(1+ tan^2 theta)^2 + cottheta/(1+ cot^2 theta)^2 = sin theta cos theta`
`sqrt((1-cos theta)/(1+cos theta)) = (cosec theta - cot theta)`
If tan A =` 5/12` , find the value of (sin A+ cos A) sec A.
Prove the following identity :
`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq
If m = a secA + b tanA and n = a tanA + b secA , prove that m2 - n2 = a2 - b2
Without using trigonometric table , evaluate :
`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Prove that:
tan (55° + x) = cot (35° – x)
Prove that :(sinθ+cosecθ)2+(cosθ+ secθ)2 = 7 + tan2 θ+cot2 θ.
If sec θ + tan θ = m, show that `(m^2 - 1)/(m^2 + 1) = sin theta`
Prove that : `1 - (cos^2 θ)/(1 + sin θ) = sin θ`.
Prove that `( tan A + sec A - 1)/(tan A - sec A + 1) = (1 + sin A)/cos A`.
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
If cosec A – sin A = p and sec A – cos A = q, then prove that `("p"^2"q")^(2/3) + ("pq"^2)^(2/3)` = 1
Prove that `(1 + sec theta - tan theta)/(1 + sec theta + tan theta) = (1 - sin theta)/cos theta`
`1/sin^2θ - 1/cos^2θ - 1/tan^2θ - 1/cot^2θ - 1/sec^2θ - 1/("cosec"^2θ) = -3`, then find the value of θ.
