Question

If $\sec \theta =\frac{13}{5}$, show that $\frac{2\sin \theta -3\cos \theta }{4\sin \theta -9\cos \theta }=3$.

Answer 1

Given:

To show that

Now, we know that

Therefore,

Therefore,

…… (1)

Now, we know that

…… (2)

Now, by comparing equation (1) and (2)

We get,

= 5

And

Hypotenuse = 13

Therefore from above figure

Base side

Hypotenuse

Side AB is unknown, It can be determined by using Pythagoras theorem

Therefore by applying Pythagoras theorem

We get,

Therefore by substituting the values of known sides

We get,

Therefore,

Therefore,

…… (3)

Now, we know that

Now from figure (a)

We get,

Therefore,

…… (4)

Now L.H.S. of the equation to be proved is as follows

Substituting the value of and from equation (1) and (4) respectively

We get,

Therefore,

Hence proved that,