Advertisements
Advertisements
Question
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Advertisements
Solution
Consider `cos^2 25^circ + cos^2 65^circ`
⇒ `cos^2(90^circ - 65^circ) + cos^2 65^circ`
⇒ `sin^2 65^circ + cos^2 65^circ = 1`
APPEARS IN
RELATED QUESTIONS
Prove the following identities:
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (1 + cosA)/sinA`
`1+((tan^2 theta) cot theta)/(cosec^2 theta) = tan theta`
If a cos θ + b sin θ = 4 and a sin θ − b sin θ = 3, then a2 + b2 =
Prove the following identity :
`sec^2A + cosec^2A = sec^2Acosec^2A`
Prove the following identity :
`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`
Prove the following identity :
`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`
Prove that:
`(sin A + cos A)/(sin A - cos A) + (sin A - cos A)/(sin A + cos A) = 2/(2 sin^2 A - 1)`
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that: `cos^2 A + 1/(1 + cot^2 A) = 1`.
Prove the following that:
`tan^3θ/(1 + tan^2θ) + cot^3θ/(1 + cot^2θ)` = secθ cosecθ – 2 sinθ cosθ
