How do you simplify # sec^2x (1-sin^2x)#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Trevor Ryan. Oct 12, 2015 1 Explanation: From trig identities, #sin^2x+cos^2x=1# #therefore 1-sin^2x=cos^2x# #therefore sec^2x(1-sin^2x)=sec^2x*cos^2x# #=1/(cos^2x)*cos^2x# #=1# 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 21788 views around the world You can reuse this answer Creative Commons License