Question

Evaluate the following:
(i) cos 15º.cos 25º.cos 30º.cosec 65º.cosec 75º.​

Answer 1

Step-by-step explanation:

what is the answer???????

Answer 2

Hey there!

Given,

$\displaystyle \cos 15^o . \cos 25^o . \cos30^o . cosec \ 65^o . cosec \ 75^o\\\\=\cos 15^o . \cos 25^o . \cos30^o.\dfrac{1}{\sin 65^o} . \dfrac{1}{sin 75^o}\\\\=\cos 15^o . \cos 25^o . \cos30^o.\dfrac{1}{\sin(90^o-25^o) }. \dfrac{1}{\sin(90^o-15^o)}\\\\=\cos 15^o . \cos 25^o . \cos30^o . \dfrac{1}{\cos 25^o} . \dfrac{1}{\cos 15^o}\\\\\sf On \ canceling \ cos 15^o \ and \ cos 25^o:\\\\=\cos 30^o\\\\=\dfrac{\sqrt{3}}{2}$

Formulas used:

• sin (90 - Ф) = cos Ф

• $cosec \ \theta = \dfrac{1}{\sin \theta}$