Question

Prove the following trigonometric identities:
6.) sec(theta)/tan(theta)=csc(theta)

(3 different)
Calculation | reason

Answer 1

Convert everything to terms of sine and cosine:

$\dfrac{\sec\theta}{\tan\theta}=\dfrac{\frac1{\cos\theta}}{\frac{\sin\theta}{\cos\theta}}$

The factors of $\dfrac1{\cos\theta}$ cancel to give

$\dfrac1{\sin\theta}=\csc\theta$

Answer 2

The trigonometric identity is $\rm \dfrac{Sec\theta}{Tan\theta}=Cosec\theta$.

We have to prove the following trigonometric identities:

Trigonometric ratios;

These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

Given

Prove the statement;

$\rm \dfrac{Sec\theta}{Tan\theta}=Cosec\theta$

Here, sec theta and tan theta can be written as;

$\rm Sec\theta=\dfrac{1}{Cos\theta}\\\\Tan\theta=\dfrac{Sin\theta}{Cos\theta}$

Substitute the values in the equation

$\rm = \rm \dfrac{Sec\theta}{Tan\theta}\\\\=\dfrac{\dfrac{1}{cos\theta}}{\dfrac{sin\theta}{cos\theta}}\\\\=\dfrac{1}{cos\theta}\times {\dfrac{sin\theta}{cos\theta}\\\\={\dfrac{1}{sin\theta}\\\\=cosec\theta$

Therefore, The trigonometric identity is $\rm \dfrac{Sec\theta}{Tan\theta}=Cosec\theta$.

Hence proved.

To know more about trigonometric identity click the link given below.

https://brainly.com/question/22698523