Question

if cot q=1/√3 then show that 1-cos square q /2-sin square q =3/5

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Answer 1

Step-by-step explanation:

We have,

cotq = 1 / root3

We know that cot 60° = 1 / root3

So, cotq = cot 60°

Therefore, q = 60°

LHS : 1 - cos^2q / 2 - sin^2q

= 1 - cos(60°)^2 / sin(60°)^2

= 1 - (1/2)^2 / 2 - (root3/2)^2

= (1 - 1/4) / (2 - 3/4)

= ( 3/4 ) / ( 5/4 )

= 3/5 = RHS

Hence, LHS = RHS (proved)