Math, asked by athravshandilyakota, 2 months ago

sinQ /1-cot Q + cos Q / 1 - tan Q
(a) 0
(b) 1
(c) sin 0 + coso (d) sino - cos O
The value of (1 + cota​

Answers

Answered by axyx
1

Answer:

  • idk

Step-by-step explanation:

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Answered by MrImpeccable
4

ANSWER:

To Solve:

\:\:\:\bullet\:\:\:\dfrac{\sin\theta}{1-\cot\theta}+\dfrac{\cos\theta}{1-\tan\theta}

Solution:

We are given that,

\implies\dfrac{\sin\theta}{1-\cot\theta}+\dfrac{\cos\theta}{1-\tan\theta}

We know that,

\hookrightarrow\cot\theta=\dfrac{\cos\theta}{\sin\theta}

And,

\hookrightarrow\tan\theta=\dfrac{\sin\theta}{\cos\theta}

So,

\implies\dfrac{\sin\theta}{1-\frac{\cos\theta}{\sin\theta}}+\dfrac{\cos\theta}{1-\frac{\sin\theta}{\cos\theta}}

Taking LCM in the denominators of both the fractions,

\implies\dfrac{\sin\theta}{\frac{\sin\theta-cos\theta}{\sin\theta}}+\dfrac{\cos\theta}{\frac{\cos\theta-sin\theta}{\cos\theta}}

On simplifying,

\implies\dfrac{\sin^2\theta}{\sin\theta-cos\theta}+\dfrac{\cos^2\theta}{\cos\theta-sin\theta}

\implies\dfrac{\sin^2\theta}{\sin\theta-cos\theta}+\dfrac{\cos^2\theta}{-(\sin\theta-cos\theta)}

Hence,

\implies\dfrac{\sin^2\theta}{\sin\theta-cos\theta}-\dfrac{\cos^2\theta}{\sin\theta-cos\theta}

On simplifying,

\implies\dfrac{\sin^2\theta-\cos^2\theta}{\sin\theta-cos\theta}

We know that,

\hookrightarrow a^2-b^2=(a+b)(a-b)

Hence,

\implies\dfrac{(\sin\theta-\cos\theta)(\sin\theta+\cos\theta)}{\sin\theta-cos\theta}

On simplifying,

\implies\bf{sin\theta+cos\theta}

Hence, option c is correct.

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