If sec(t) = 3, how do you find the exact value of #tan^2 (t)#? Trigonometry Right Triangles Relating Trigonometric Functions 1 Answer moutar Jan 10, 2016 8 Explanation: #sin^2t+cos^2t=1# If we divide this identity by #cos^2t# we get: #tan^2t+1=sec^2t# If #sect=3# then: #tan^2t+1=9# #tan^2t=8# 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 3954 views around the world You can reuse this answer Creative Commons License