Question

Sin⁡θ + cos⁡θ = √(3 ) , then prove that tan⁡θ + cot⁡θ =1

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

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$\huge{ \boxed{ \purple{ \mathfrak{given = > }}}}$

$\large \: { \green{sin \theta + cos \: \theta = \sqrt{3} }}$

$\huge{ \boxed{ \red{ \mathfrak{solution = > }}}}$

$\large \blue{squaring \: on \: both \: side}$

${sin}^{2} \theta + {cos}^{2} \theta + 2sin\theta.cos\theta = 3$

$\large \boxed{ \purple {{sin}^{2} \theta + {cos}^{2} \theta = 1}}$

$1 + 2sin\theta.cos\theta = 3 \\ \\ 2sin\theta.cos\theta = 2 \\ \\ sin\theta.cos\theta = 1..........................(1)$

So,

$\large \: tan \: \theta + cot\theta$

${ \pink{ \boxed{tan\theta = \frac{sin\theta}{cos\theta} }}} \\ \\ { \pink{ \boxed{cot\theta = \frac{cos\theta}{sin \theta}}}}$

$= > \frac{sin\theta}{cos\theta} + \frac{cos\theta}{sin\theta} \\ \\ = > \frac{ {sin}^{2}\theta + {cos}^{2} \theta }{sin\theta.cos\theta} \\ \\ = > \frac{1}{sin\theta.cos\theta} \\ \\ = \frac{1}{1} \: \: \: \: \: \: \: \: \: \: (by \: equation \: (1) \\ \\ { \boxed{ \purple{hence \: proved \: \: tan\theta + cot\theta = 1}}}$

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