Question

without using a calculator, find the value of sin^2 (32º) + cos^2 (32º) - sin (85º)/cos (5º)

Answer 1

Answer:

as you know..

$sin { \alpha \: }^{2} + cos { \alpha}^{2} = 1$

sin^2(32°)+cos^2(32°)-sin(85°)/cos(5°)

= 1-sin(90-5)/cos(5°)

= 1-cos(5°)/cos(5°). [sin(90-5)°=cos(5°), complementary angle]

= 1-1 =0