Advertisements
Advertisements
प्रश्न
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cot^2 A(sec A - 1))/(1 + sin A) = sec^2 A ((1 - sin A)/(1 + sec A))`
Given that:
(1 + cos α) (1 + cos β) (1 + cos γ) = (1 − cos α) (1 − cos α) (1 − cos β) (1 − cos γ)
Show that one of the values of each member of this equality is sin α sin β sin γ
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
cosec4θ − cosec2θ = cot4θ + cot2θ
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
Prove that `(cos(90 - "A"))/(sin "A") = (sin(90 - "A"))/(cos "A")`
Prove that sec2θ + cosec2θ = sec2θ × cosec2θ
If cos A = `(2sqrt("m"))/("m" + 1)`, then prove that cosec A = `("m" + 1)/("m" - 1)`
