Advertisements
Advertisements
Question
Prove the following identities:
`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`
Solution
L.H.S. = `(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA)`
= `((sinA + cosA)^2 + (sinA - cosA)^2)/((sinA - cosA)(sinA + cosA))`
= `(sin^2A + cos^2A + 2sinAcosA + sin^2A + cos^2A - 2sinA cosA)/(sin^2A - cos^2A)`
= `(2(sin^2A + cos^2A))/(sin^2A - cos^2A)`
= `2/(sin^2A - cos^2A)` ...[sin2A + cos2A = 1]
= `2/(sin^2A - cos^2A)`
= `2/(sin^2A - (1 - sin^2A))`
= `2/(2sin^2A - 1)` = R.H.S.
APPEARS IN
RELATED QUESTIONS
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`
`(tan^2theta)/((1+ tan^2 theta))+ cot^2 theta/((1+ cot^2 theta))=1`
`(1+ tan theta + cot theta )(sintheta - cos theta) = ((sec theta)/ (cosec^2 theta)-( cosec theta)/(sec^2 theta))`
Write True' or False' and justify your answer the following :
The value of the expression \[\sin {80}^° - \cos {80}^°\]
Evaluate:
sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot2 30°
Prove that :
2(sin6 θ + cos6 θ) − 3 (sin4 θ + cos4 θ) + 1 = 0
Prove the following identities.
`sqrt((1 + sin theta)/(1 - sin theta)` = sec θ + tan θ
Choose the correct alternative:
sec2θ – tan2θ =?
`5/(sin^2theta) - 5cot^2theta`, complete the activity given below.
Activity:
`5/(sin^2theta) - 5cot^2theta`
= `square (1/(sin^2theta) - cot^2theta)`
= `5(square - cot^2theta) ......[1/(sin^2theta) = square]`
= 5(1)
= `square`
Prove that cosec θ – cot θ = `sin theta/(1 + cos theta)`
