Question #480a9 Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer Gerardina C. Jul 6, 2016 #-sin^2x# Explanation: Since #1-sin^2x=cos^2x# and #secx=1/cosx# you have #(1-sin^2x)(1-sec^2x)=# #cos^2x(1-1/cos^2x)=# #cancel(cos^2x)(cos^2x-1)/cancel(cos^2x)=# #-sin^2x# 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 1419 views around the world You can reuse this answer Creative Commons License