Question

If A = tan 6° tan 42° & B = cot 66° cot 78° , then

(1) A = 2B 

(2) A = 1/3

(3) A = B 

(4) 3A = 2B

Answer 1

Correct option (3) A = B

Explanation :

A = tan 6° tan 42° & B = cot 66° cot 78°

\(\frac{A}{B}\) = tan 6° tan 42° tan 66° tan 78°

\(\frac{A}{B}=\frac{(sin66^°\,sin6^°)(sin78^°\,sin42^°)}{(cos66^°\,cos6^°)(cos78^°\,cos42^°)}\)

Comments

What is the identity used in second step?

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We use the following identities
Cos C - Cos D=2sin(C+D)/2 sin (D-C)/2
Cos C + Cos D=2cos(C+D)/2 cos (C-D)/2