Question

7. The value of cos 15° x cos 45° 2 cosec 75°
is?​

Answer 1

Answer:

cos 15° x cos 45° 2 cosec 75°

Answer 2

The value of $\cos 15 \times cos 45 \times 2\csc 75$ = $\sqrt{2}$

Step-by-step explanation:

We have,

$\cos 15 \times cos 45 \times 2\csc 75$

To find, the value of $\cos 15 \times cos 45 \times 2\csc 75$ = ?

∴ $\cos 15 \times cos 45 \times 2\csc (90-15)$

Using trigonometric identity,

$\sec A=\csc (90-A)$

$=\cos 15 \times \dfrac{1}{\sqrt{2}} \times 2\sec 15$

Using trigonometric identity,

$cos 45=\dfrac{1}{\sqrt{2}}$

$=\cos 15 \times \dfrac{1}{\sqrt{2}} \times 2\dfrac{1}{\cos 15}$

Using trigonometric identity,

$\sec A=\dfrac{1}{\cos A}$

= $\sqrt{2}$

∴ The value of $\cos 15 \times cos 45 \times 2\csc 75$ = $\sqrt{2}$