Question

The value of the expression Cosec(75°+theetha)-(15°-theetha)-tan(55°+theetha)+cot(35°-theetha)


plz give me answer fastly​

Answer 1

GIVEN :

$\sf{Cosec(75°+ \theta )-(15°- \: \theta)-tan(55°+ \theta)+cot(35°- \theta) }$

TO FIND :

find the value

SOLUTION :

$\sf{Cosec(75°+ \theta )-(15°- \: \theta)-tan(55°+ \theta)+cot(35°- \theta) }$

Using,

★ cosec A = sec (90° - A)

★ cot A = tan (90°- A)

$\sf{ : \implies \: \sec (\: 90 \degree \: - [75°+ \theta ])- \sec (15°- \: \theta)-tan(55°+ \theta)+ \tan(90 \degree -[35 \degree - \theta]) }$

$\sf{ : \implies \: \sec (\: 90 \degree \: - 75°+ \theta )- \sec (15°- \: \theta)-tan(55°+ \theta)+ \tan(90 \degree -35 \degree - \theta) }$

$\sf{ : \implies \: \sec (\: 15 \degree \: - \theta )- \sec (15°- \: \theta)-tan(55°+ \theta)+ \tan(50\degree - \theta) }$

$\sf{ : \implies \: 0}$

hence the required value is 0

Answer 2

❍᭄Given:-

$\tt{Cosec(75°+ \theta )-(15°- \: \theta)-tan(55°+ \theta)+cot(35°- \theta) }$

❍᭄To Find:-

The value of expression

❍᭄Solution

$\tt{Cosec(75°+ \theta )-(15°- \: \theta)-tan(55°+ \theta)+cot(35°- \theta) }$

By Using:-

• cosec A = sec (90° - A)
• cot A = tan (90°- A)

$\tt{ \purple: \longmapsto\: \sec (\: 90 \degree \: - [75°+ \theta ])- \sec (15°- \: \theta)-tan(55°+ \theta)+ \tan(90 \degree -[35 \degree - \theta]) }$

$\tt{\purple : \longmapsto \: \sec (\: 90 \degree \: - 75°+ \theta )- \sec (15°- \: \theta)-tan(55°+ \theta)+ \tan(90 \degree -35 \degree - \theta) }$

$\tt{ \purple: \longmapsto \: \sec (\: 15 \degree \: - \theta )- \sec (15°- \: \theta)-tan(55°+ \theta)+ \tan(50\degree - \theta) }$

$\sf{ \purple: \longmapsto \: 0}$

∴ The value of the expression is 0

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