Advertisements
Advertisements
प्रश्न
Prove that: `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`.
Prove the following:
`(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ) = tan θ`
Advertisements
उत्तर
LHS = `(sin θ - 2sin^3 θ)/(2 cos^3 θ - cos θ)`
= `(sin θ(1 - 2sin^2 θ))/(cos θ(2 cos^2 θ - 1))`
= `(tan θ(1 - 2(1 - cos^2 θ)))/(2 cos^2θ - 1 )`
= `(tan θ(1 - 2 + 2 cos^2 θ))/(2 cos^2θ - 1 )`
= `(tan θ(2 cos^2 θ - 1))/(2 cos^2θ - 1 )`
= tan θ
= RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
Express the ratios cos A, tan A and sec A in terms of sin A.
Evaluate sin25° cos65° + cos25° sin65°
Prove the following trigonometric identities.
`sqrt((1 - cos A)/(1 + cos A)) = cosec A - cot A`
Prove the following trigonometric identities.
`(cos theta - sin theta + 1)/(cos theta + sin theta - 1) = cosec theta + cot theta`
`(sin theta)/((sec theta + tan theta -1)) + cos theta/((cosec theta + cot theta -1))=1`
If `sin theta = 1/2 , " write the value of" ( 3 cot^2 theta + 3).`
Simplify
sin A `[[sinA -cosA],["cos A" " sinA"]] + cos A[[ cos A" sin A " ],[-sin A" cos A"]]`
prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`
Prove that: 2(sin6 θ + cos6 θ) – 3 (sin4 θ + cos4 θ) + 1 = 0.
Prove that (sec θ + tan θ) (1 – sin θ) = cos θ
