Advertisements
Advertisements
प्रश्न
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Advertisements
उत्तर
L.H.S. = `sqrt((1 + sin theta)/(1 - sin theta)`
= `sqrt(((1 + sin theta)(1 + sin theta))/((1 - sin theta)(1 + sin theta))` ...[conjugate (1 − sin θ)]
= `sqrt((1 + sin theta)^2/(1 - sin^2 theta)`
= `sqrt((1 + sin theta)^2/(cos^2 theta)`
= `(1 + sin theta)/(cos theta)`
= `1/cos theta + sin theta/cos theta`
= sec θ + tan θ
L.H.S. = R.H.S.
APPEARS IN
संबंधित प्रश्न
Prove the following trigonometric identities.
`(cos^2 theta)/sin theta - cosec theta + sin theta = 0`
Prove the following trigonometric identities.
`(cot A + tan B)/(cot B + tan A) = cot A tan B`
Prove the following identities:
sec2A + cosec2A = sec2A . cosec2A
If `cosA/cosB = m` and `cosA/sinB = n`, show that : (m2 + n2) cos2 B = n2.
Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`
What is the value of 9cot2 θ − 9cosec2 θ?
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
Prove that (sin θ + cosec θ)2 + (cos θ + sec θ)2 = 7 + tan2 θ + cot2 θ.
sec2θ – tan2θ = ?
Prove that `(1 + sec A)/(sec A) = (sin^2A)/(1 - cos A)`.
