Question

Plz help by solving 5 .a.
Salute u if u solved it

Answer 1

Answer:

$cos2\alpha=sin4\beta$

Step-by-step explanation:

Given:

$tan\alpha=\frac{1}{7}$

$tan\beta=\frac{1}{3}$

$cos2\alpha$

$=\frac{1-tan^2\alpha}{1+tan^2\alpha}$

$=\frac{1-(\frac{1}{7})^2}{1+(\frac{1}{7})^2}$

$=\frac{1-\frac{1}{49}}{1+\frac{1}{49}}$

$=\frac{\frac{49-1}{49}}{\frac{49+1}{49}}$

$=\frac{\frac{48}{49}}{\frac{50}{49}}$

$=\frac{48}{50}$

$=\frac{24}{25}$.............(1)

$sin4\beta$

$=sin2(2\beta)$

$=2\:sin2\beta\:cos2\beta$

$=2(\frac{2\:tan\beta}{1+tan^2\beta})(\frac{1-tan^2\beta}{1+tan^2\beta})$

$=2(\frac{2(\frac{1}{3})}{1+(\frac{1}{3})^2})(\frac{1-(\frac{1}{3})^2}{1+(\frac{1}{3})^2})$

$=2(\frac{\frac{2}{3}}{1+\frac{1}{9}})(\frac{1-\frac{1}{9}}{1+\frac{1}{9}})$

$=2(\frac{\frac{2}{3}}{\frac{10}{9}})(\frac{\frac{8}{9}}{\frac{10}{9}})$

$=(\frac{\frac{4}{3}}{\frac{10}{9}})(\frac{8}{10})$

$=(\frac{12}{10})(\frac{8}{10})$

$=\frac{96}{100}$

$=\frac{24}{25}$.............(2)

From (1) and (2)

$cos2\alpha=sin4\beta$