Question

If tan a = c/d
prove that d cos 2a + c sin 2a = d.
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Answer 1

tan(a) = c/d

d*sin(a) = c*cos(a) ----------------------> 1

Since sin(2A) = 2 sin(A)cos(A)

Multiply both sides of 1 with 2 sin(a)

2d*sin²(a) = c*sin(2a) ----------------> 2

Now the question says d*cos(2a) + c*sin(2a) = d to be proved,

Substituting 2, we have

d*cos(2a) + 2d*sin²(a) as LHS

Since, cos(2A) = cos²(A) - sin²(A)

d*(cos²(a) - sin²(a)) + 2d*sin²(a)

d*cos²(a) + d*sin²(a)

d(cos²(a) + sin²(a))

d.

Hence LHS = RHS is proved.