Advertisements
Advertisements
Question
Prove the following trigonometric identities.
`(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
Advertisements
Solution
We have to prove `(1 - cos theta)/sin theta = sin theta/(1 + cos theta)`
We know that, `sin^2 theta + cos^2 theta = 1`
Multiplying both numerator and denominator by `(1 + cos theta)`, we have
`(1 - cos theta)/sin theta = ((1 - cos theta)(1 + cos theta))/(sin theta(1 + cos theta))`
`= (1 - cos^2 theta)/(sin theta(1 + cos theta))`
` = (sin^2 theta)/(sin theta(1 + cos theta))`
`= sin theta/(1 + cos theta)`
APPEARS IN
RELATED QUESTIONS
If `sec alpha=2/sqrt3` , then find the value of `(1-cosecalpha)/(1+cosecalpha)` where α is in IV quadrant.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined:
`cos A/(1 + sin A) + (1 + sin A)/cos A = 2 sec A`
Prove the following trigonometric identities.
(1 + tan2θ) (1 − sinθ) (1 + sinθ) = 1
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 trigonometric identities.
`tan theta/(1 - cot theta) + cot theta/(1 - tan theta) = 1 + tan theta + cot theta`
Prove the following identities:
`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`
Prove the following identities:
`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`
`sin^2 theta + 1/((1+tan^2 theta))=1`
If `(x/a sin a - y/b cos theta) = 1 and (x/a cos theta + y/b sin theta ) =1, " prove that "(x^2/a^2 + y^2/b^2 ) =2`
Write the value of `(1 + cot^2 theta ) sin^2 theta`.
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Prove the following identity :
`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`
Find A if tan 2A = cot (A-24°).
If tan θ = 2, where θ is an acute angle, find the value of cos θ.
If tan α = n tan β, sin α = m sin β, prove that cos2 α = `(m^2 - 1)/(n^2 - 1)`.
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
The value of sin2θ + `1/(1 + tan^2 theta)` is equal to
If 5 sec θ – 12 cosec θ = 0, then find values of sin θ, sec θ
Prove that sin4A – cos4A = 1 – 2cos2A
