Question

Prove this identity: Θ$\frac{1+cos\alpha }{sin\alpha ^{2} } = \frac{1}{1-cos\alpha }$

Answer 1

Step-by-step explanation:

1+sin^a/cos^a=1/1-cos^2LHS = Cos A/(1+ sin A) + (1+ sin A)/cos A

= begin mathsize 16px style fraction numerator cosA over denominator 1 plus sinA end fraction plus fraction numerator 1 plus sinA over denominator cosA end fraction end style

= begin mathsize 16px style fraction numerator cos squared straight A plus open parentheses 1 plus sinA close parentheses squared over denominator cosA open parentheses 1 plus sinA close parentheses end fraction end style

= begin mathsize 16px style fraction numerator cos squared straight A plus 1 plus 2 sinA plus sin squared straight A over denominator cosA open parentheses 1 plus sinA close parentheses end fraction end style

= begin mathsize 16px style fraction numerator 1 plus 1 plus 2 sinA over denominator cosA open parentheses 1 plus sinA close parentheses end fraction end style

= begin mathsize 16px style fraction numerator 2 open parentheses 1 plus sinA close parentheses over denominator cosA open parentheses 1 plus sinA close parentheses end fraction end style

= begin mathsize 16px style 2 over cosA equals 2 secA end style

Proove that (CotA+CosecA-1)/(CotA-CosecA+1) = (1+CosA)/SinA

maths sums

prove that cos theta by 1-tan theta+sin theta by 1- cot theta equals to sin theta+ cos theta

Cosec(theta) - cot(theta) = alpha then cosec(theta)+ cot( alpha)=?

(1+secA)/secA = sin²A/(1-cosA)