Question

if tan theeta =1 prove that 2 sin theeta cos thesta =1​

Answer 1

Answer:

tan theta= 1, implies theta is 45° therefore LHS= 2sintheta cos theta

2 X sin45° cos45°

2 X 1/√2 X 1/√2

= 1 = RHS

HENCE PROVED

Answer 2

Step-by-step explanation:

assume this ¢ to be theta

Given,

tan¢ = 1............(1)

we know that,

tan45=1.............(2)

by comparing eq(1) with eq(2)

tan¢ = tan45*

=} ¢ = 45* .............(3)

To prove :-

2sin¢ cos¢ = 1

in eq(3) we know that ¢=45*,

so now by substituting the value of ¢ we get,

2sin(45)×cos(45)=1

2 × 1/√2 × 1/√2 = 1

2/(√2 × √2) = 1

2/2 = 1

1 = 1

since LHS = RHS,

2 sin ¢ cos ¢ =1.

hope it helped you

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