# If sin x + cos x = a, find the value of sin6 x + cos6 x.

Given, sin x + cos x = a

We need to find the value of the expression,

sin6 x + cos6 x = (sin2 x)3 + (cos2 x)3

= (sin2 x + cos2 x)3 – 3 sin2 x cos2 x (sin2 x + cos2 x)

[ by using the formula a3 + b3 = (a+b)3 – 3ab(a+b)]

= (1)3 – 3 sin2 x cos2 x (1)

[ by using the formula sin2 x + cos2 x = 1]  [ by using the formula sin2 x + cos2 x = 1]    Hence sin6 x + cos6 x 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  Trigonometric Functions - 0152 mins  Graphs of trigonometric ratios | Trigonometric Identities39 mins  Trigo ratios for compound angles48 mins  Quiz on Graph of Trigonometric Ratios40 mins  Conditional Identities31 mins  Transformation formula in compound angles | Interactive Quiz37 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 