Question

If tan=1 find (
sin×sin-cos×cos)

Answer 1

Answer:

From the given we can calculate the value of required expression as follow:-)

Given that

$tan \theta = 1 \\ \implies{tan}^{2} \theta = 1$

As we know that

${sec}^{2} \theta = 1 + {tan}^{2} \theta \\ \implies {sec}^{2} \theta = 1 + 1 = 2$

Now ;

Also

${cos}^{2} \theta = \frac{1}{ {sec}^{2}\theta} \\ \implies {cos}^{2}\theta = \frac{1}{2} \: \: \: \: \: .................(i)$

Now , As we know that

${sin}^{2} \theta = 1 - {cos}^{2} \theta \\ \implies {sin}^{2} \theta = 1 - \frac{1}{2} = \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: ...........(ii)$

As we have to calculate the value of

$sin\theta \times sin\theta - cos\theta \times cos\theta \\ that \: is \: \\ {sin}^{2} \theta - {cos}^{2} \theta$

$Now , using (i) \: and(ii) \\ {sin}^{2} \theta - {cos}^{2}\theta \\ \: = \frac{1}{2} - \frac{1}{2} \\ = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ANSWER }}$

Answer 2

Answer:

As

[tex]tan \theta = 1 \\ \implies \: \theta = 45 \degree[/tx]

Now

[tex] {sin}^{2} 45 - {cos}^{2} 45 \\ = \frac{1}{2} - \frac{1}2 \\ = 0 ...