Question

If tan a is equal to root 2 minus 1 then prove that sin a cos a is equal to 1 by 2 root 2 is equal to root 2 by 4

Answer 1

Here is your ans, follow this way of process you will definitely answer all these types of trigonometry proofs.

Answer 2

Answer:

Given : $tan a = \sqrt{2} - 1$

To prove : $sin a\times cos a = \frac{1}{2\sqrt{2}}= \frac{\sqrt{2}}{4}$

Since, $sec^2a =tan^2 a + 1$

⇒ $sec^2a =( \sqrt{2} - 1 )^2 + 1$

⇒ $sec^2 a = 2 + 1 - 2\sqrt{2} + 1 = 4 - 2\sqrt{2}$

$\frac{tana}{sec^2a}=\frac{\sqrt{2}-1}{(4-2\sqrt{2})}$

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

$\frac{tana}{sec^2a}=\frac{1}{2\sqrt{2}}$

$\frac{sina /cosa}{1/cos^2a}=\frac{1}{2\sqrt{2}}$

$sin a \times cos a = =\frac{1}{2\sqrt{2}}$

$sin a \times cos a = \frac{\sqrt{2}}{4}$ ( by rationalization )

Hence, proved.