Question

can someone please help me solve this?

Answer 1

Answer:

$\implies\dfrac{sec\theta + tan\theta}{cot\theta+cos\theta} = tan\theta sec\theta$

Step-by-step explanation:

$\implies\dfrac{sec\theta + tan\theta}{cot\theta+cos\theta}$

From the trigonometric properties :

• cotA = 1 / tanA
• cosA = 1 / secA

$\implies\dfrac{sec\theta+tan\theta}{\dfrac{1}{tan\theta}+\dfrac{1}{sec\theta}}\\\\\\\implies\dfrac{sec\theta+tan\theta}{\dfrac{sec\theta+tan\theta}{tan\theta sec\theta}}\\\\\\\implies\dfrac{sec\theta+tan\theta}{1}\times\dfrac{sec\theta tan\theta}{sec\theta + tan\theta} \\\\\\\implies tan\theta sec\theta$

Hence proved.

Answer 2

$\huge{\mathfrak{\underline{\underline{\orange{Answer :-}}}}}$

To prove :-

$\large{\bf{\frac{sec\theta + tan\theta}{cot\theta+cos\theta} = tan\theta {\times}sec\theta}}$

Proof :-

Using Identities :-

$\huge{\boxed{\underline{\red{cotA = \frac{1}{tanA}}}}}$

$\huge{\boxed{\underline{\blue{cosA = \frac{1}{secA}}}}}$

________________[Put Values]

$\sf{\frac{sec\theta+tan\theta}{\frac{1}{tan\theta}+\frac{1}{sec\theta}}}$

Taking LCM

$\sf{\frac{sec\theta+tan\theta}{\frac{sec\theta+tan\theta}{tan\theta sec\theta}}}$

$\sf{\frac{sec\theta+tan\theta}{1}\times\frac{sec\theta tan\theta}{sec\theta + tan\theta}}$

$\bf{tan\theta{\times} sec\theta}$

$\huge{\boxed{\boxed{\underline{\bf{\red{Hence \: Proved}}}}}}$