pt tan(π/4+ theta)+tan(π/4-theta=2sec2theta
Answers
Answered by
1
Step-by-step explanation:
tan(pi/4+theta) + tan(pi/4-theta)
=tan(pi/4)+tan(theta)/1-tan(pi/4)*tan(theta) + tan(pi/4)-tan(theta)/1-tan(pi/4)*tan(theta)
= 1+tan(theta)/1-tan(theta) + 1-tan(theta)/1+tan(theta)
= 1+tan²(theta)+2tan(theta)+1+tan²(theta)-2tan(theta)/1-tan²(theta)
= 2+2tan²(theta)/1-tan²(theta)
= 2sec²(theta)/1-tan²(theta)
= 2/cos²(theta)-sin²(theta)
= 2/cos(2theta)
= 2sec(2theta)
Similar questions