Question

If A = 45º show that : cos 2A = 1-2 sin^2 A = 2 cos^2 A-1​
Class 11, Chapter 4, Trigonometric Functions, Exercise 4(A)

Answer 1

Given: A$=45\textdegree$

To show that $cos\ 2A=1-2sin^{2}A=2cos^{2}A-1$

Solution,

The given equation has three sides, all three sides need to be satisfied

L.H.S $A=45\textdegree$

       $2A=2\times45\textdegree$

             $=90\textdegree$

    $cos\2A=cos90\textdegree$

             $=0$

R.H.S $2cos^{2}A-1$

$=2(cos45)^{2}-1$

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

$=2(\frac{1}{\sqrt{2}})-1$

Both the $2$ get canceled

$=1-1$

$=0$

Solving the middle term

$1-2sin^{2}A$

$=1-2(sin45)^{2}$

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

Both the $2$ get canceled

$=1-1$

$=0$

Final Answer: As all the three terms are $0$. Hence verified.