Answer to Question #88547 in Trigonometry for Adams

Question

Evaluate 1-2cos²25/(1-2sin²65)

Answer 1

Evaluate 1-2cos²25/(1-2sin²65)

Solution:

$$1- (2cos⁡^225\circ)/(1-2sin⁡^265\circ) =$$ $$=1-(2(1+cos⁡50\circ)/2)/cos⁡130\circ =$$ $$=1-(1+cos⁡50\circ)/(-cos⁡50\circ ) =$$ $$=1+(1+cos⁡50\circ)/cos⁡50\circ =$$ $$=1+1/cos⁡50\circ +cos⁡50\circ/cos⁡50\circ =$$ $$=1+1+1/cos⁡50\circ =2+1/cos⁡50\circ ≈3.55572$$

Answer: 3.55572