Question

[6]
If cos 0 = sin 0, then the value of 2 tan2 e
+ cos2 0 - 1 is
-3
A
(B) 1
2
3
(C)
(D)
3
(A)
2
دیا | M
(
EX​

Answer 1

$\sf \pink{Given:}$

if cos theta=sin theta, then value of 2 tan^2 thetha+cos^2 thetha-1 is?

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$\sf \pink{Solution:}$

$sinθ = cosθ \\ 2 \: tan {}^{2}θ = cos θ \\ then \: θ = 45°$

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$2 \: \: tan {}^{2} 45° + sin {}^{2} \: 45° - 1 \\ 2(1 {)}^{2} + ( 1/\sqrt{2}) {}^{2} - 1 \\ 2 \times 1 + 1/2 \\ = 3/2$

$\sf \pink{Answer:}$

Option [C] 3/2

Answer 2

$\textbf{\large{\red{Question}} }$

$\implies$ $If \:cos\:theta\:=\:sin\:theta\:,\:then\:value\:of\:2\:tan²\:theta+cos²theta-1\:is\:?$

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$\large \blue{\underline{\underline{Solution}}}$

$\implies$$sinθ = cosθ$

$\implies$$2tan²θ= cosθ$

$\implies$$then\:θ= 45°$

$\implies$ $2tan²45° + sin²45° - 1$

$\implies$ 2(1)² +$\dfrac{1}²{√2}$ - 1

$\implies$ 2 × 1 + $\dfrac{1}{√2}$

$\implies$ $\dfrac{3}{2}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}$

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ㅤ$\textbf{\huge{\green{Answer}} }$

ㅤㅤㅤOption C $\dfrac{3}{2}$