Q. 17

# Prove the following identities:cos 4x = 1 – 8 cos2 x + 8 cos4 x

To prove: cos 4x = 1 – 8 cos2 x + 8 cos4 x

Proof:

Take LHS:

cos 4x

Identities used:

cos 2x = = 2 cos2 x – 1

Therefore,

= 2 cos2 2x – 1

= 2(2 cos2 2x – 1)2 – 1

= 2{(2 cos2 2x}2 + 12 – 2×2 cos2 x} – 1

= 2(4 cos4 2x + 1 – 4 cos2 x) – 1

= 8 cos4 2x + 2 – 8 cos2 x – 1

= 8 cos4 2x + 1 – 8 cos2 x

= RHS

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Ratios of Sub Angles35 mins
Trigonometric Functions - 0568 mins
Trigonometry ratios of allied angles | Interactive Quiz38 mins
Conditional Identities31 mins
Transformation formula in compound angles | Interactive Quiz37 mins
Trigonometric Functions - 0152 mins
Graphs of trigonometric ratios | Trigonometric Identities39 mins
Trigo ratios for compound angles48 mins
Quiz on Graph of Trigonometric Ratios40 mins
Trigonometric Functions - 0658 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses