Question

evaluate cosec 25 degree - sec 65 degree ​

Answer 1

GIVEN :-

• Cosec 25° - sec 65° .

TO FIND :-

• The value of Cosec 25° - sec 65° .

SOLUTION :-

☛ For the above value of cosec 25° and sec 65°. See the trigonometric ratio chart.

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

☛ From the about trigonometric ratios chart we get the value of,

◉ cosec 25° = 7.55

◉ sec 65° = 2

☛ Now we have to find the value of Cosec 25° - sec 65° . so let's substitute the above values,

➬ Cosec 25° - sec 65° .

➬ 7.55 - 2

➬ 5.55

Hence the value of Cosec 25° - sec 65° is 5.55.

ADDITIONAL INFORMATION :-

◉ Some some trigonometry formulas ,

➬ sin θ = Opposite side/Hypotenuse.

➬ cos θ = Adjacent side/Hypotenuse.

➬ tan θ = Perpendicular/Base.

➬ tan θ = sin θ/cos θ

Answer 2

Answer:

cosec 25° = 7.55}

                              (from trigonometric ratio chart)

sec 65°     = 2 }    

NOW,

➬ Cosec 25° - sec 65° .

= 7.55 - 2

=5.55