Advertisements
Advertisements
प्रश्न
Prove that `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2 = sin A.cos A`
Advertisements
उत्तर
LHS = `tan A/(1 + tan^2 A)^2 + cot A/(1 + cot^2 A)^2`
= `tan A/(sec^2 A)^2 + cot A/(cosec^2 A)^2`
= `sin A/cos A xx cos^2 A xx cos^2 A + cos A/sin A xx sin^2 A xx sin^2 A`
= sin A.cos3A + sin3A.cos A
= sin A cos A (cos2 A + sin2 A)
= sin A. cos A x 1
= sin A. cos A
= RHS
Hence proved.
संबंधित प्रश्न
Prove the following trigonometric identities.
sec6 θ = tan6 θ + 3 tan2 θ sec2 θ + 1
Prove the following identities:
`(sintheta - 2sin^3theta)/(2cos^3theta - costheta) = tantheta`
Show that : `sinAcosA - (sinAcos(90^circ - A)cosA)/sec(90^circ - A) - (cosAsin(90^circ - A)sinA)/(cosec(90^circ - A)) = 0`
` (sin theta - cos theta) / ( sin theta + cos theta ) + ( sin theta + cos theta ) / ( sin theta - cos theta ) = 2/ ((2 sin^2 theta -1))`
If m = ` ( cos theta - sin theta ) and n = ( cos theta + sin theta ) "then show that" sqrt(m/n) + sqrt(n/m) = 2/sqrt(1-tan^2 theta)`.
Write the value of `(1 - cos^2 theta ) cosec^2 theta`.
Write the value of `(1+ tan^2 theta ) ( 1+ sin theta ) ( 1- sin theta)`
Write the value of cosec2 (90° − θ) − tan2 θ.
Prove the following identities: sec2 θ + cosec2 θ = sec2 θ cosec2 θ.
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
