SOLUTION: prove that 15tan^2 +4sec^2 = 23

Algebra ->  Trigonometry-basics -> SOLUTION: prove that 15tan^2 +4sec^2 = 23      Log On


   

Question 792275: prove that 15tan^2 +4sec^2 = 23
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
prove that 15tan^2(x) +4sec^2(x) = 23
solve for x:
15+tan%5E2%28x%29%2B4sec%5E2%28x%29=23
15+%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29%2B%284%2Fcos%5E2%28x%29%29=23
%2815+sin%5E2%28x%29%2B4%29%2F%28cos%5E2%28x%29%29=23
15+sin%5E2%28x%29%2B4=23+cos%5E2%28x%29
15+sin%5E2%28x%29%2B4=23%281-sin%5E2%28x%29%29
15+sin%5E2%28x%29%2B4=23-23sin%5E2%28x%29
38+sin%5E2%28x%29=19
sin^2(x)=19/38=1/2
sin(x)=√1/√2
x=π/4
Check:
15tan^2(x)=15tan^2(π/4)15*1=15
4sec^2(x)=4/cos^2(π/4)=4/(1/2)=8
15tan^2(x)+15tan^2(x)=15+8=23
Given identity is true if x=π/4