Advertisements
Advertisements
प्रश्न
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
उत्तर
LHS = `sec^2A.cosec^2A = 1/(cos^2A.sin^2A)`
RHS = `tan^2A + cot^2A + 2 = tan^2A + cot^2A + 2tan^2A.cot^2A`
= `(tanA + cotA)^2 = (sinA/cosA + cosA/sinA)^2`
= `((sin^2A + cos^2A)/(sinA.cosA))^2 = 1/(cos^2A.sin^2A)`
= Hence , LHS = RHS
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following identities:
(sec A – cos A) (sec A + cos A) = sin2 A + tan2 A
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
Write the value of ` cosec^2 (90°- theta ) - tan^2 theta`
If \[\sin \theta = \frac{1}{3}\] then find the value of 2cot2 θ + 2.
If \[\sin \theta = \frac{1}{3}\] then find the value of 9tan2 θ + 9.
Express (sin 67° + cos 75°) in terms of trigonometric ratios of the angle between 0° and 45°.
Prove the following identities.
sec4 θ (1 – sin4 θ) – 2 tan2 θ = 1
Prove that `[(1 + sin theta - cos theta)/(1 + sin theta + cos theta)]^2 = (1 - cos theta)/(1 + cos theta)`
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
