Advertisements
Advertisements
Question
Prove the following identities.
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
Advertisements
Solution
`(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
L.H.S = `(cot theta - cos theta)/(cot theta + cos theta)`
= `cos theta/sin theta - cos theta ÷ cos theta/sin theta + cos theta`
= `(cos theta - sin theta cos theta)/sin theta ÷ (cos theta + sin theta cos theta)/sin theta`
= `(cos theta(1 - sin theta))/sin theta ÷ (cos theta(1 + sin theta))/sin theta`
= `(cos theta(1 - sin theta))/sin theta xx sin theta/(cos theta(1 + sin theta))`
= `(1 - sin theta)/(1 + sin theta)`
R.H.S = `("cosec" - 1)/("cosec"+1)`
= `1/sin theta - 1 ÷ 1/sin theta+ 1`
= `(1 - sin theta)/sin theta ÷ (1 + sin theta)/sin theta`
= `(1 - sin theta)/sin theta xx sin theta/(1 + sin theta)`
= `(1 - sin theta)/(1 + sin theta)`
R.H.S = L.H.S ⇒ `(cot theta - cos theta)/(cot theta + cos theta) = ("cosec" theta - 1)/("cosec" theta + 1)`
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities
(1 + cot2 A) sin2 A = 1
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`
Without using trigonometric identity , show that :
`cos^2 25^circ + cos^2 65^circ = 1`
Prove that `((1 - cos^2 θ)/cos θ)((1 - sin^2θ)/(sin θ)) = 1/(tan θ + cot θ)`
cot θ . tan θ = ?
If tan α + cot α = 2, then tan20α + cot20α = ______.
(tan θ + 2)(2 tan θ + 1) = 5 tan θ + sec2θ.
If `sqrt(3) tan θ` = 1, then find the value of sin2θ – cos2θ.
Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec2 A – 1
