Question

Question 38
If
cosa + cos B = m and sin a +sin B =n then​

Answer 1

Given

[math]m=\frac{\cos\alpha}{\cos\beta}[/math] & n[math]=\frac{\cos\alpha}{\sin\beta}[/math]

hence,

[math](m^2+n^2)\cos^2\beta=\left(\left(\frac{\cos\alpha}{\cos\beta}\right)^2+\left(\frac{\cos\alpha}{\sin\beta}\right)^2\right)\cos^2\beta[/math]

[math]=\left(\frac{\cos^2\alpha}{\cos^2\beta}+\frac{\cos^2\alpha}{\sin^2\beta}\right)\cos^2\beta[/math]

[math]=\cos^2\alpha\left(\frac{1}{\cos^2\beta}+\frac{1}{\sin^2\beta}\right)\cos^2\beta[/math]

[math]=\cos^2\alpha\left(\frac{\sin^2\beta+\cos^2\beta}{\cos^2\beta\sin^2\beta}\right)\cos^2\beta[/math]

[math]=\cos^2\alpha\left(\frac{1}{\sin^2\beta}\right)[/math]

[math]=\frac{\cos^2\alpha}{\sin^2\beta}[/math]

[math]=\left(\frac{\cos\alpha}{\sin\beta}\right)^2[/math]

[math]=n^2[/math]

hope it helps you