Question

If , show that sin θ (1 − tan θ).

Answer 1

Given: ……(1)

To show that

Now, we know that …… (2)

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

We get,

= 12

And

Hypotenuse = 13

Therefore from above figure

Base side

Hypotenuse

Side AB is unknown and 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, we know that

Now from figure (a)

We get,

Therefore,

…… (5)

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

…… (6)

Substituting the value of and from equation (4) and (5) respectively

We get,

Taking L.C.M inside the bracket

We get,

Therefore,

Now, by opening the bracket and simplifying

We get,

…… (7)

From equation (6) and (7) , it can be shown that