Question

prove that sinA- sin^3A/ 2cos^3 A- cos A = tanA

Answer 1

hope you understand...

Answer 2

♧♧HERE IS YOUR ANSWER♧♧

Trigonometry is the study of angles and its ratios. This study prescribes the relation amongst the sides of a triangle and angles of the triangle.

There are sine, cosine, tangent, cot, sectant and cosec ratios to an angle of a triangle.

Let me tell you an interesting fact about Trigonometry.

"Triangle" > "Trigonometry"

Remember some formulae now :

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1

Want to learn more!

Here it is :

sin(A + B) = sinA cosB + cosA sinB

sin(A - B) = sinA cosB - cosA sinB

cos(A + B) = cosA cosB - sinA sinB

cos(A - B) = cosA cosB + sinA sinB

SOLUTION :

L.H.S.

$= \frac{sin \alpha - 2 {sin}^{3} \alpha }{2 {cos}^{3} \alpha - cos \alpha } \\ \\ = \frac{sin \alpha (1 - 2 {sin}^{2} \alpha )}{cos \alpha (2 {cos}^{2} \alpha - 1) } \\ \\ = \frac{sin \alpha \times cos2 \alpha }{cos \alpha \times cos2 \alpha } \\ \\ = \frac{sin \alpha }{cos \alpha } \\ \\ = tan \alpha$

= R.H.S. [Proved]

RULE :

1 - 2 sin²α = cos2α
2 cos²α - 1 = cos2α

♧♧HOPE IT HELPS YOU♧♧