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The value of {{cosec} }^{ 2 }{ 67 }^{ o }-{ }^{ 2 }{ 23 }^{

Question

The value of $cosec^{2} 67^{o} - tan^{2} 23^{o}$ is :

2

0

1

3

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The value of

cosec^{2} 67^{o} - tan^{2} 23^{o}

is :

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Text solutionVerified

cosec^{2} 67^{o} - tan^{2} 23^{o} = 1 + cot^{2} 67^{o} - tan^{2} 23^{o}

[∵ cosec^{2} θ = 1 + cot^{2} θ]

= 1 + cot^{2} (90^{o} - 23^{o}) - tan^{2} 23^{o}

= 1 + tan^{2} 23^{o} - tan^{2} 23^{o} = 1 + 0 = 1

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