Advertisements
Advertisements
प्रश्न
If A = 30°, verify that `sin 2A = (2 tan A)/(1 + tan^2 A)`.
Advertisements
उत्तर
LHS = sin 2A
Putting A = 30° in LHS and RHS., we get
LHS = sin 2 x 30° = sin 60° = `sqrt3/2`
RHS = `(2 xx tan 30°)/(1 + tan^2 30°) = (2 xx 1/sqrt3)/( 1 + (1/sqrt3)^2)`
= `(2/sqrt3)/(1 + 1/3). (2/sqrt3)/(4/3)`
= `(2 xx 3)/(sqrt3 xx 4) = sqrt3/4`
Hence,
LHS = RHS
Hence proved.
संबंधित प्रश्न
Prove the following identities:
`cotA/(1 - tanA) + tanA/(1 - cotA) = 1 + tanA + cotA`
`cos^2 theta /((1 tan theta))+ sin ^3 theta/((sin theta - cos theta))=(1+sin theta cos theta)`
Show that none of the following is an identity:
`cos^2theta + cos theta = 1`
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
Prove the following identity :
`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`
Prove the following identities:
`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`
Prove that cot2θ × sec2θ = cot2θ + 1.
If sinθ – cosθ = 0, then the value of (sin4θ + cos4θ) is ______.
tan θ × `sqrt(1 - sin^2 θ)` is equal to:
Let x1, x2, x3 be the solutions of `tan^-1((2x + 1)/(x + 1)) + tan^-1((2x - 1)/(x - 1))` = 2tan–1(x + 1) where x1 < x2 < x3 then 2x1 + x2 + x32 is equal to ______.
