Question #34291 Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer P dilip_k Dec 27, 2016 #sin^4x+cos^4x# #=(sin^2x+cos^2x)^2-2sin^2xcos^2x# #=1-2sin^2xcos^2x# #=1-1/2xx4sin^2xcos^2x# #=1-1/2xx(2sinxcosx)^2# #=1-1/2xx((sinx+cosx)^2-(sin^2x+cos^2))^2# #=1-1/2xx(a^2-1)^2# #=(2-(a^2-1)^2)/2# #=(2-a^4+2a^2-1)/2# #=(1-a^4+2a^2)/2# Answer link Related questions What does it mean to find the sign of a trigonometric function and how do you find it? What are the reciprocal identities of trigonometric functions? What are the quotient identities for a trigonometric functions? What are the cofunction identities and reflection properties for trigonometric functions? What is the pythagorean identity? If #sec theta = 4#, how do you use the reciprocal identity to find #cos theta#? How do you find the domain and range of sine, cosine, and tangent? What quadrant does #cot 325^@# lie in and what is the sign? How do you use use quotient identities to explain why the tangent and cotangent function have... How do you show that #1+tan^2 theta = sec ^2 theta#? See all questions in Relating Trigonometric Functions Impact of this question 3344 views around the world You can reuse this answer Creative Commons License