Question

If √2 sin θ = 1, find the value of sec^2 θ - cosec^2 θ.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

$\sqrt{2 }\sin( \alpha ) = 1 \\ \sin( \alpha ) = 1 \div \sqrt{2} \\ \csc( \alpha ) = \sqrt{2} \div 1 \\ we \: know \: that \: \\ \cos( \alpha ) = 1 \div \sqrt{2} ....{.from \: trigo \: table \: } \\ therefor \: sec{ \alpha } = \sqrt{2} \div 1 \\ \\ \sec^{2} \alpha - \csc^{2} \alpha = \cos {}^2 (1 \div \alpha ) - \sin {}^{2} (1 \div \alpha ) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1 \div \sqrt{2} - 1 \div \sqrt{2 } = 0$
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