3. Given tan 0 = 2, where 0° SO < 90°. Determine the following i terms of t: Lan (23) (a) sec 0 (b) cot 0 (c) cos20 (d) tan2 0 - sec20
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Now Consider the RHS
\begin{gathered}=\dfrac{1}{\tan \theta + \cot\theta}\\=\dfrac{1}{\frac{\sin\theta}{\cos\theta} +\frac{\cos\theta}{\sin\theta}}\\\\=\dfrac{\cos\theta\sin\theta}{{\sin^2\theta}+{\cos^2\theta}}\\\\=\cos\theta\sin\theta\end{gathered}
=
tanθ+cotθ
1
=
cosθ
sinθ
+
sinθ
cosθ
1
=
sin
2
θ+cos
2
θ
cosθsinθ
=cosθsinθ
LHS=RHS
Hence, proved
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Prove this trigonometric identities
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