Advertisements
Advertisements
Question
Prove the following identity :
`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`
Advertisements
Solution
LHS = `cosA/(1 - tanA) + sinA/(1 - cotA)`
= `cosA/(1-sinA/cosA) + sinA/(1 - cosA/sinA) = cosA/((cosA -sinA)/cosA) + sinA/((sinA - cosA)/sinA)`
= `cos^2A/(cosA - sinA) + sin^2A/(sinA - cosA) = (cos^2A - sin^2A)/((cosA - sinA))`
`((cosA - sinA)(cosA + sinA))/(cosA - sinA)`
= sinA + cosA = RHS
APPEARS IN
RELATED QUESTIONS
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following identities:
`1/(secA + tanA) = secA - tanA`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
`(cos theta cosec theta - sin theta sec theta )/(costheta + sin theta) = cosec theta - sec theta`
If cos \[9\theta\] = sin \[\theta\] and \[9\theta\] < 900 , then the value of tan \[6 \theta\] is
Prove the following identity :
`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`
If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`
Without using trigonometric identity , show that :
`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`
Choose the correct alternative:
1 + cot2θ = ?
Prove that `costheta/(1 + sintheta) = (1 - sintheta)/(costheta)`
