Question

evaluate cos/sec+cosec ​

Answer 1

Answer:

cos ÷sec+cosec

change the following in the terms of sin & cos

cos÷(1÷cos+1÷sin)

by taking LCM

cos ÷(sin+cos÷sincos)

cos(sincos) ÷ sin+cos

Answer 2

The value of $\dfrac{\cos \theta}{\sec \theta+\csc \theta}$ = $\dfrac{1}{{\sin \theta(\sin \theta+\cos \theta)}}$

Step-by-step explanation:

We have,

$\dfrac{\cos \theta}{\sec \theta+\csc \theta}$

To find, the value of $\dfrac{\cos \theta}{\sec \theta+\csc \theta}$ = ?

∴ $\dfrac{\cos \theta}{\sec \theta+\csc \theta}$

= $\dfrac{\cos \theta}{\dfrac{1}{\cos \theta} +\dfrac{1}{\sin \theta} }$

Using the trigonometric identity,

$\sec A= \dfrac{1}{\cos A}$ and $\csc A= \dfrac{1}{\sin A}$

= $\dfrac{\cos \theta}{\dfrac{\sin \theta+\cos \theta}{\sin \theta\cos \theta}}$

= $\dfrac{\cos \theta}{{\sin \theta\cos \theta(\sin \theta+\cos \theta)}}$

= $\dfrac{1}{{\sin \theta(\sin \theta+\cos \theta)}}$

Thus, the value of $\dfrac{\cos \theta}{\sec \theta+\csc \theta}$ = $\dfrac{1}{{\sin \theta(\sin \theta+\cos \theta)}}$