Evaluate :1+cosθ1-cosθ
To evaluate :1+cosθ1-cosθ
1+cosθ1-cosθ=(1+cosθ)×(1+cosθ)(1-cosθ)×(1+cosθ) ( Rationalizing the denominator)
=(1+cosθ)2(1)2-(cosθ)2 [Formula used: a2-b2=(a+b)(a-b)]
=(1+cosθ)(1-cos2θ)
=(1+cosθ)sin2θ [Formula used: sin2θ+cos2θ=1]
=(1+cosθ)sinθ
= 1sinθ+cosθsinθ
=cosecθ+cotθ [Formula used :1sinθ=cosecθ and cosθsinθ=cotθ]
Thus, the simplified form of 1+cosθ1-cosθ=cosecθ+cotθ
Evaluate the expression when x=-45andy=13
2x+6y
loge(n+1)−loge(n−1)=4a[(1n)+(13n3)+(15n5)+...∞] Find 8a.