Question

Sin (90-0) + cos (90-0 sin (90-0)/
Tan (90-0)
بے​

Answer 1

Topic:-

Trigonometry

Question:-

$\frac{ \sin (90 - \theta) + \cos(90 - \theta ) \sin( 90 - \theta ) }{ \tan(90 - \theta ) }$

Solution:-

$sin(90 - \theta) = cos \theta \\ cos(90 - \theta) = sin \theta \\ tan(90 - \theta) = cot \theta$

$now \: substitute \: all \: formulas \: in \: the \: given \: question$

$= \frac{cos \theta + sin \theta \: cos \theta }{tan \theta}$

$= \frac{cos \theta }{tan \theta } + \frac{sin \theta \: cos \theta }{tan \theta}$

$cot \theta + \frac{ \frac{sin \theta \: cos \theta }{sin \theta } }{cos \theta }$

$cot \theta + sin \theta \: cos \theta \times \frac{cos \theta }{sin \theta }$

$cot \theta + {cos}^{2} \theta$

Answer:-

$cot \theta + {cos}^{2} \theta$

Know More:-

Trigon metric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

csc²θ - cot²θ = 1

Trigometric relations

sinθ = 1/cscθ

cosθ = 1 /secθ

tanθ = 1/cotθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Trigonmetric ratios

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

cotθ = adj/opp

cscθ = hyp/opp

secθ = hyp/adj

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