Question

if root 3 tan theta equals to 3 sin theta, then find the value of sin square theta-cos square theta.

Answer 1

√3 tanФ = 3 sinФ

Squaring both sides

3 tan²Ф = 9 sin²Ф

3(sin²Ф/cos²Ф) = 9 sin²Ф          [∵ tanФ = sinФ/cosФ]

Dividing both sides by sin²Ф

3/cos²Ф = 9

cos²Ф = 3/9

cos²Ф = 1/3 ------- ( i )

Further

1 - sin²Ф = 1/3        [ ∵ cos²Ф = 1 - sin²Ф]

sin²Ф = 1 - 1/3

sin²Ф = 2/3 --------- ( ii )

∴ sin²Ф - cos²Ф = 2/3 - 1/3            [from ( i ) and ( ii )]

                          = 1/3

Answer 2

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