Question

find the value of tan 2A, if cos 3A = sin 45.

Answer 1

Here is the solution
=================

cos 3A = sin 45
sin(90 - 3A) = sin 45

90 - 3A = 45

90 - 45 = 3A

45 = 3A

=> A = 45/3 = 15

Now, Tan 2A = Tan (2*15) = Tan 30 = 1/√3 = 0.5773

Hope it helps......

Answer 2

cos 3A = sin 45
sin ( 90 - 3A ) = sin 45
∵ cos ∅ = sin ( 90 - ∅)

∴ 90- 3A = 45
∴ 3A = 45
∴  A = 15° .

Now, sin 2A = sin 2*15 = sin 30 = 1/2

and

cos 2A = cos 2*15 = cos 30 = √3 / 2

Now, tan 2A = sin 2A / cos 2A
= [1/2] / [ √3/2]
= 1/√3

∴ tan 2A = 1/√3.

Hope this helps you !
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