Question

Trignometry: Evaluate: Cos20 . Cos35 Cos45 cosec 55 cos 70

Answer 1

Given: The trigonometric term  Cos 20 . Cos 35 Cos 45 cosec 55 cos 70

To find: The value of the given term.

Solution:

• Now we have given Cos 20 Cos 35 Cos 45 cosec 55 cos 70

• We can rewrite it as:

                   Cos 20 Cos 35 Cos 45 cosec (90 - 35) cos (90 - 20)

• Now we know that :

                   cosec(90 - x) = sec x

                   cos(90 - x) = sin x

• Applying this, we get:

                   Cos 20 Cos 35 Cos 45 Sec 35 Sin 20

                   Cos 20 Cos 35  (1/√2)  Sec 35 Sin 20

• Now we know that cos x × sec x = 1, applying this, we get:

                   Cos 20 x Sin 20 x 1 x (1/√2)

                   Cos 20 x Sin 20 / √2

Answer:

         So the final value is Cos 20 x Sin 20 / √2.

Answer 2

Here is your answer........