Advertisements
Advertisements
Question
Prove the following identity :
`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`
Solution
= `sqrt((1 + cosA)/(1 - cosA) . (1 + cosA)/(1 + cosA))`
= `sqrt((1 + cosA)^2/(1 - cos^2A)) = sqrt((1 + cosA)^2/sin^2A)`
= `sqrt((1 + cos^2A)/sinA) = sqrt(1/sinA + cos^2A/sinA)`
= `sqrt((cosecA + cot^2A)`
= cosecA + cotA
APPEARS IN
RELATED QUESTIONS
Evaluate without using trigonometric tables:
`cos^2 26^@ + cos 64^@ sin 26^@ + (tan 36^@)/(cot 54^@)`
Prove the following trigonometric identities.
tan2θ cos2θ = 1 − cos2θ
Prove the following trigonometric identities.
`(1 - sin theta)/(1 + sin theta) = (sec theta - tan theta)^2`
Prove the following trigonometric identities.
sec A (1 − sin A) (sec A + tan A) = 1
Prove the following identities:
`cot^2A((secA - 1)/(1 + sinA)) + sec^2A((sinA - 1)/(1 + secA)) = 0`
` (sin theta + cos theta )/(sin theta - cos theta ) + ( sin theta - cos theta )/( sin theta + cos theta) = 2/ ((1- 2 cos^2 theta))`
Write True' or False' and justify your answer the following :
The value of \[\cos^2 23 - \sin^2 67\] is positive .
\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to
Prove that `(sin θ tan θ)/(1 - cos θ) = 1 + sec θ.`
Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`
