Advertisements
Advertisements
Question
Prove the following identities:
sec4 A (1 – sin4 A) – 2 tan2 A = 1
Advertisements
Solution
sec4 A (1 – sin4 A) – 2 tan2 A
= sec4 A – sec4 A sin4 A – 2 tan2 A
= `(sec^2A)^2 - 1/(cos^4A)sin^4A - 2tan^2A`
= (1 + tan2 A)2 – tan4 A – 2 tan2 A ...`[(sec^2A - tan^2A = 1), (sec^2A = 1 + tan^2A)]`
= (1)2 + (tan2 A)2 – 2 × 1 × tan2 A – tan4 A – 2 tan2 A
= 1 + tan4 A + 2 tan2 A – tan4 A – 2 tan2 A
= 1
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
`(1-cos^2theta) sec^2 theta = tan^2 theta`
Prove the following identities:
`(cos theta "cosec" theta - sin theta sec theta )/(cos theta + sin theta) = "cosec" theta - sec theta`
If `secθ = 25/7 ` then find tanθ.
The value of sin2 29° + sin2 61° is
If cos A + cos2 A = 1, then sin2 A + sin4 A =
Prove the following identity :
`sec^4A - sec^2A = sin^2A/cos^4A`
Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`
Evaluate:
sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot2 30°
If sin θ + cos θ = a and sec θ + cosec θ = b , then the value of b(a2 – 1) is equal to
