Question

cot theta + tan theta is equal to cosec theta sec theta prove that
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Answer 1

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➠ Prove that : cotθ + tanθ = (cosecθ)(secθ)

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❏ Trigonometry is one of the most important topic in modern mathematics that is useful in various field.

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❏ Here are simple formulas used frequently

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$\bold {:\leadsto \; sin\theta = \dfrac{1}{cosec\theta} }$

$\bold {:\leadsto \; cos\theta = \dfrac{1}{sec\theta} }$

$\bold {:\leadsto \; tan\theta = \dfrac{1}{cot\theta} }$

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Let's Start !

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Let's simply with help of our basic knowledge.

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$\bold { \orange{:\implies cot\theta + tan\theta } }$

$\bold {:\implies \dfrac{cos\theta}{sin\theta} + \dfrac{sin\theta}{cos\theta} }$

$\bold {:\implies \dfrac{cos^2\theta + sin^2\theta}{(sin\theta \;\times\; cos\theta)} }$

$\bold { \red{:\implies \dfrac{1}{sin\theta \;\times\; cos\theta} \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \{\because sin^2\theta + cos^2\theta = 1 \} } }$

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$\bold{:\implies \dfrac{1}{sin\theta} \; \times \; \dfrac{1}{cos\theta} }$

$\bold {:\implies cosec\theta\; \times \; sec\theta }$

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∴ LHS = RHS

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Hence proved.

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Hope this helps u.../

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