Question

The value of the expression cos1∘cos2∘cos3∘.......cos179∘ is
(A) 0
(B) 1
(C) 1√2
(D) −1

Answer 1

EXPLANATION.

Value of the expression.

⇒ cos1° cos2° cos3° . . . . . cos179°.

As we know that,

⇒ cos(0°) = 0.

Now, we can write expression as,

⇒ cos1° cos2° cos3° . . . . . cos89° cos90° . . . . . cos178° cos179°.

As we can see that,

⇒ cos1° cos2° cos3° . . . . . cos89° x 0 . . . . . cos178° cos179°.

⇒ 0.

Hence, Option [A] is correct answer.

                                                                                                               

MORE INFORMATION.

(1) sin²θ + cos²θ = 1.

(2) 1 + tan²θ = sec²θ

(3) 1 + cot²θ = cosec²θ.