CBSE Class 10 Math Question Paper 2018 | Q27

Question 27: Prove that: \\frac{sin A - 2 sin^3 A}{2cos^3 A - cos A}) = tan A

Video Explanation

Explanatory Answer | CBSE Class 10 Math Paper 2018 Q27

LHS : \\frac{sin A - 2 sin^3 A}{2cos^3 A - cos A})
Take sin A common in the numerator and cos A common in the denominator. \\frac{sin A (1 - 2 sin^2 A)}{cos A (2 cos^2 A - 1)})
We know sin² A + cos ² A = 1.
Rewrite 1 in both the numerator and denominator of the expression as sin² A + cos ² A
= \\frac{sin A(sin^2 A + cos^2 A - 2 sin^2 A)}{cos A(2 cos^2 A - sin^2 A - cos^2 A )})
= \\frac{sin A (cos^2 A - sin^2 A) }{cos A (cos^2 A - sin^2 A)}) = \\frac{\text{sin A}}{\text{cos A}})
= tan A