Question

evaluate 2×sin 43/cos 47-cot 30/tan 60 -root 2sin45

Answer 1

2*sin(90-47)/cos47 -cot(90-60)/tan60 -root 2*1/root2   (sin45=1/root2)
2*cos47/cos47 -tan60/tan60 -1
2*1-1-1
2-1-1
0

Answer 2

Concept:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names. The adjacent side, opposite side, and hypotenuse side of the right triangle are used to define each of these trigonometric ratios. The six trigonometric ratios are the source of all fundamental trigonometric identities.

sin(90-A)=cos A

Cos(90-A) = snA

tan(90-A) =cot A

cot(90-A) =tanA

TanA=1/cotA

Given:

2×sin 43/cos 47-cot 30/tan 60 - √2sin45

Find:

2×sin 43/cos 47-cot 30/tan 60 - √2sin45

Solution:

=2sin(90-47)/cos47 -cot(90-60)/tan60 -√2*1/√2   (∵sin45=1/√2)

=2cos47/cos47 -tan60/tan60 -1

=2*1-1-1

=2-1-1

=0

Therefore,the answer is 0

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