Question

complete the following activity to prove sin^theta / cos theta + cos theta = sec theta
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Answer 1

SOLUTION :-

$\\ \\ \tt \: lhs = \frac{ {sin}^{2} \theta}{cos \theta} + cos \theta \\ \\ \\ \sf \: cross \: multiplying....we \: get... \\ \\ \\ \implies\tt \: \frac{ {sin}^{2} \theta + {cos}^{2} \theta }{cos \theta} \\ \\ \\ \bigstar\boxed{ \bf \: {sin}^{2} \theta + {cos}^{2} \theta= 1 } \\ \\ \\ \implies\tt \: \frac{1}{cos \theta} \\ \\ \\ \bigstar\boxed{ \bf \: \frac{1}{cos \theta} = sec \theta } \\ \\ \\ \implies \tt \: sec \theta = rhs \: \: \: \: \: \: \: \: \: \sf \: \{verified \}$

MORE IDENTITIES :-

$\\ \bigstar \bf \: \frac{1}{sin \theta} = cosec \theta \\ \\ \\ \bigstar \bf \: \frac{1}{tan \theta} = cot \theta \\ \\ \\ \bigstar \bf \: 1 + {tan}^{2} \theta = {sec}^{2} \theta \\ \\ \\ \bigstar \bf \: 1 + {cot}^{2} \theta = {cosec}^{2} \theta$