Question

If A = B = 60°, verify that

(i) cos (A − B) = cos A cos B + sin A sin B
(ii) sin (A − B) = sin A cos B − cos A sin B
(iii) $\tan \left(A-B\right)=\frac{\tan A-\tan B}{1+\tan A\tan B}$

Answer 1

(i) Given:

…… (1)

To verify:

…… (2)

Now consider left hand side of the expression to be verified in equation (2)

Therefore,

Now consider right hand side of the expression to be verified in equation (2)

Therefore,

Hence it is verified that,

(ii) Given:

…… (1)

To verify:

…… (2)

Now consider LHS of the expression to be verified in equation (2)

Therefore,

Now by substituting the value of A and B from equation (1) in the above expression

We get,

Hence it is verified that,

(iii) Given:

…… (1)

To verify:

…… (2)

Now consider LHS of the expression to be verified in equation (2)

Therefore,

Now consider RHS of the expression to be verified in equation (2)

Therefore,

Now by substituting the value of A and B from equation (1) in the above expression

We get,

Hence it is verified that,