If √ 3 tan = 3 sin , find the value of sin^2 theta - cos^2 theta
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since root 3 tan theta = 3sin theta
so, root 3 son theta /cos theta= sin theta
= so, root 3 will cut 3 and sin theta wil be cancelled
= so, 1/cos theta= root3
so, cos theta =1/root 3
so, squaring on both sides:
=cos2theta= 1/3
let it be equation no. 1
= 1-sin2theta= 1/3
=sin 2 theta=1-1/3
= sin2theta=2/3
let it be equation no. 2
so, on subtracting equation 1 from 2:
sin2theta - cos2theta = 22/32 - 12/32
= 4/9 - 1/9
= 3/9 = 1/3 that is the answer.
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Answer:
since root 3 tan theta = 3sin theta so, root 3 son theta /cos theta= sin theta = so, root 3 will cut 3 and sin theta wil be cancelled = so, 1/cos theta= root3 so, cos theta =1/root 3 so, squaring on both sides: =cos2theta= 1/3 let it be equation no. 1 = 1-sin2theta= 1/3 =sin 2 theta=1-1/3 = sin2theta=2/3 let it be equation no. 2 so, on subtracting equation 1 from 2: sin2theta - cos2theta = 22/32 - 12/32 = 4/9 - 1/9 = 3/9 = 1/3 that is the answer.
Step-by-step explanation:
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