Question

Hello..!!! guys a difficult one !!! ----- If tan = a / b , then prove that b sec ¤ / a cosec¤ = 1 ​

Answer 1

Answer:

Sorry I didn't know answer of this question

Answer 2

Given:

$\tan \theta=\frac{a}{b}$

Solution:

$\frac{b \sec \theta}{a \csc \theta}=1$

According to trigonometric function, the secant is the inverse of cosine.

$\sec \theta=\frac{1}{\cos \theta}$

According to trigonometric function, the cosecant is inverse of sine.

$\csc \theta=\frac{1}{\sin \theta}$

On applying, both the trigonometric function in the given expression,

$\Rightarrow \frac{b \sec \theta}{a \csc \theta}=\frac{b\left(\frac{1}{\cos \theta}\right)}{a\left(\frac{1}{\sin \theta}\right)}$

On taking reciprocal,

$\Rightarrow \frac{b \sec \theta}{a \csc \theta}=\frac{b \sin \theta}{a \cos \theta}$

Now, the above expression becomes,

$\Rightarrow \frac{b \sec \theta}{a \csc \theta}=\frac{b}{a} \times \frac{\sin \theta}{\cos \theta}$

From question, on substituting the value of tangent,

$\Rightarrow \frac{b \sec \theta}{a \csc \theta}=\frac{b}{a} \times \frac{a}{b}$

On cancelling values,

$\therefore \frac{b \sec \theta}{a \csc \theta}=1$

Hence proved.