Question

If tan θ = 1 ; then the value of (sin²θ - cos²θ) is :​

Answer 1

Given:-

$\red{➤}\:$$\sf \tan \theta = 1$

To Find:-

$\orange{☛}\:$$\sf Value \:of\:(sin²θ - cos²θ) \_\: \_\: \_\: (1)$

Solution:-

$\begin{gathered}\\\quad\longrightarrow\quad \sf \tan\theta= 1 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf \tan\theta= tan \:45⁰ \\\end{gathered}$

$\underline{\tt\pink{Comparing\:both\:sides-}}$

$\green{ \underline { \boxed{ \sf{\theta = 45⁰}}}}$

$\underline{\tt\pink{Putting \:Values\: in\: (1)-}}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf (sin²45⁰ - cos²45⁰) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf ((\frac{1}{√2})^2 - (\frac{1}{√2})^2) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf (\frac{1}{2} - \frac{1}{2}) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 0 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow \boxed{\sf { (sin² \theta - cos² \theta) =0}}\end{gathered}$

Alternate Method -

$\begin{gathered}\\\quad\longrightarrow\quad\sf \tan\theta = 1 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf \frac{\sin\theta}{\cos\theta} = 1 \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\sf \sin\theta = \cos \theta\_\: \_\: \_\: (2) \\\end{gathered}$

$\underline{\tt\purple{Taking\: (1)-}}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf (sin²\theta - cos²\theta) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf (sin²\theta - sin²\theta) \qquad(by \:(2)) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \boxed{\sf 0 }\\\end{gathered}$

Answer 2

$\huge\purple{\mid{\fbox{\tt{Given:}}\mid}}$

• tan$\theta$=1

$\huge\green{\mid{\fbox{\tt{To Find:}}\mid}}$

• sin²$\theta$-cos²$\theta$=?

$\huge\red{\mid{\fbox{\tt{Solution:}}\mid}}$

Given that,

tan$\theta$=1

: . $\theta$= 45°

Now, sin²$\theta$-cos²$\theta$

= sin²45°-cos²45°

= (1/2)-(1/2)

= 0

: . sin²$\theta$-cos²$\theta$=0

$\small\fbox\pink{Hope itz help uh bacchi !}$