Question

tan(1/2 cos inverse √5/3)​

Answer 1

Answer:

(3-√5)/2

Step-by-step explanation:

Given tan [1/2 cos (inverse) √5/3]

put X=cos (inverse) √5/3

cos X=√5/3

cos x=(1-tan^2(x/2))/(1+tan^2(x/2))=√5/3

3(1-tan^2(x/2))=√5(1+tan^2(x/2))

3–3tan^2(x/2)=√5+√5tan^2(x/2)

3-√5=√5tan^2(x/2)+3tan^2(x/2)

(3-√5)=(3+√5)tan^2(x/2)

tan^2(x/2)=(3-√5)/(3+√5)=(3-√5)(3-√5)/(3-√5)(3+√5)

tan^2(x/2)=(3-√5)^2/(9–5)

tan^2(x/2)=(3-√5)^2/4

tan(x/2)=(3-√5)/2

tan [1/2 cos (inverse) √5/3]=(3-√5)/2

Note:it is same as 2/(√5+3)

2/√5+3=2(√5-3)/(√5+3)(√5-3)=2(√5-3)/5–9=2(√5-3)/-4=(3-√5)/2

Answer 2

Answer:

hope it helps u

Sry for messy handwriting