Advertisements
Advertisements
Question
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Advertisements
Solution
L.H.S. = (cosec A + sin A) (cosec A – sin A)
= (cosec2 A – sin2 A) ...[∵ (a + b) (a – b) = a2 – b2]
= 1 + cot2 A – sin2 A
= cot2 A + 1 – sin2 A
= cot2 A + cos2 A ...(∵ 1 – sin2 A = cos2 A)
= R.H.S.
RELATED QUESTIONS
Prove the following trigonometric identities
`(1 + tan^2 theta)/(1 + cot^2 theta) = ((1 - tan theta)/(1 - cot theta))^2 = tan^2 theta`
Prove the following identities:
(cos A + sin A)2 + (cos A – sin A)2 = 2
Prove that:
`1/(cosA + sinA - 1) + 1/(cosA + sinA + 1) = cosecA + secA`
Prove the following identities:
(1 + tan A + sec A) (1 + cot A – cosec A) = 2
If cosec θ − cot θ = α, write the value of cosec θ + cot α.
If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`
If A = 60°, B = 30° verify that tan( A - B) = `(tan A - tan B)/(1 + tan A. tan B)`.
Prove that `(cot "A" + "cosec A" - 1)/(cot "A" - "cosec A" + 1) = (1 + cos "A")/sin "A"`
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
If 2sin2θ – cos2θ = 2, then find the value of θ.
