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prove that: 1+^{2} = ^{2}

Question

prove that:

$1 + cot^{2} θ = csc^{2} θ$

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prove that:

1 + cot^{2} θ = csc^{2} θ

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Text solutionVerified

1 + co t^{2} θ = cose c^{2} θ

L.H.S

1 + co t^{2} θ = 1 + \frac{co s ^{2} θ}{s i n ^{2} θ}

[∵ co tθ = \frac{cos θ}{s in θ}] = \frac{s i n ^{2} θ + co s ^{2} θ}{s i n ^{2} θ}

[∵ s i n^{2} θ + co s^{2} θ = 1] = \frac{1}{s i n ^{2} θ}

[∵ \frac{1}{s in θ = cosec θ}] = cose c^{2} θ

= R . H . S

∴ L . H . S = R . H . S

Hence proved

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