Question

if cot thita equal to 1 root 3 show that 1 minus cos square thita by 2 minus sin square thita equal to 3by 5

Answer 1

hiii!!!

here's ur answer...

given that cot∅ = 1/√3

we know that cot∅ = 1/tan∅

therefore 1/√3 = 1/tan∅

tan∅ = √3

tan∅ = perpendicular/base

hence, perpendicular = √3 and base = 1

hypotenuse = √(√3²)+(1)²

= √(3+1)

= √4

= 2

therefore cos∅ = base/hypotenuse = 1/2

and sin∅ = perpendicular/hypotenuse = √3/2

now, LHS :-

1 - cos²∅ / 2 - sin²∅

$= \frac{1 - {( \frac{1}{2} )}^{2} }{2 - {( \frac{ \sqrt{3} }{2}) }^{2} } \\ \\ = \frac{2 - (\frac{1}{4} )}{2 - ( \frac{3}{4}) } \\ \\ = \frac{ \frac{4 - 1}{4} }{ \frac{8 - 3}{4} } \\ \\ = \frac{ \frac{3}{4} }{ \frac{5}{4} } \\ \\ = \frac{3}{4} \times \frac{4}{5} \\ \\ = \frac{3}{5}$

RHS = 3/5

hence, LHS = RHS

hope this helps..!!