Evaluate sec² (90°-Φ) - cot²Φ / 2 (sin²25° + sin²65°)

Asked by pdcavita | 18th Nov, 2017, 01:07: PM

Expert Answer:

begin mathsize 16px style fraction numerator space sec ² space left parenthesis 90 degree minus straight capital phi right parenthesis space minus space cot ² straight capital phi space over denominator 2 space left parenthesis sin ² 25 degree space plus space sin ² 65 degree right parenthesis end fraction
equals fraction numerator cos begin display style begin display style ec end style squared end style begin display style space end style begin display style straight capital phi end style begin display style minus end style begin display style begin display style cot end style squared end style begin display style space end style begin display style straight capital phi end style over denominator 2 open square brackets sin squared left parenthesis 90 degree minus 65 degree right parenthesis plus sin squared space 65 degree close square brackets end fraction
equals fraction numerator 1 over denominator 2 open parentheses cos squared space 65 plus sin squared space 65 close parentheses end fraction
equals fraction numerator 1 over denominator 2 cross times 1 end fraction
equals 1 half end style

Answered by Rashmi Khot | 5th Dec, 2017, 04:20: PM