SOLUTION: Use the sum and difference identities to find the exact values of sine, cosine and tangent of the angle 165degrees=135degrees+30degrees

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Question 773116: Use the sum and difference identities to find the exact values of sine, cosine and tangent of the angle
165degrees=135degrees+30degrees
Answer by lwsshak3(11628) About Me  (Show Source):
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Use the sum and difference identities to find the exact values of sine, cosine and tangent of the angle 165degrees=135degrees+30degrees
sin(165º)=sin(135º+30º)=sin135º*cos30º+cos135º*sin30º=√2/2*√3/2-√2/2*1/2
=√6/4-√2/4=(√6-√2)/4
..
cos(165º)=cos(135º+30º)=cos135º*cos30º-sin135º*sin30º=-√2/2*√3/2-√2/2*1/2
=-√6/4-√2/4=(-√6-√2)/4=-(√6+√2)/4
..
tan(165º)=tan(135º+30º)=(tan135º+tan30º)/(1-tan135º*tan30º)=(-1+√3/3)/(1-(-1*√3/3)
=(-1+√3/3)/(1+√3/3)=(-3+√3)/(3+√3)