Advertisements
Advertisements
प्रश्न
Prove the following identities:
sec2 A . cosec2 A = tan2 A + cot2 A + 2
Advertisements
उत्तर
L.H.S. = sec2 A . cosec2 A
= `1/(cos^2A) * 1/(sin^2A)`
= `1/(cos^2A sin^2A)`
= `(sin^2A + cos^2A)/(cos^2A sin^2A)`
= `1/(cos^2A) + 1/(sin^2A)`
= sec2 A + cosec2 A
= 1 + tan2 A + 1 + cot2 A ...(∵ sec2 A = 1 + tan2 A and cosec2 A = 1 + cot2 A)
= tan2 A + cot2 A + 2 = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove that:
(1 + tan A . tan B)2 + (tan A – tan B)2 = sec2 A sec2 B
Prove the following identities:
`(1 - cosA)/sinA + sinA/(1 - cosA)= 2cosecA`
Prove the following identities:
`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`
`(cot ^theta)/((cosec theta+1)) + ((cosec theta + 1))/cot theta = 2 sec theta`
Verify that the points A(–2, 2), B(2, 2) and C(2, 7) are the vertices of a right-angled triangle.
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
Prove the following identities.
`costheta/(1 + sintheta)` = sec θ – tan θ
sin(45° + θ) – cos(45° – θ) is equal to ______.
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
