Question

If cot theta = 7\8, then the value of sin theta is

Answer 1

ANSWER

Given,

cotθ=

8

7

tanθ=

cotθ

1

=

7

8

We know that,

tanθ=

adjacentSide

oppositeSide

From Pythagoras theorem,

Hypotenuse

2

=OppositeSide

2

+AdjacentSide

2

Hypotenuse

2

=8

2

+7

2

Hypotenuse

2

=64+49=113

Hypotenuse=

113

sinθ=

Hypotenuse

oppositeSide

=

113

8

cosθ=

Hypotenuse

AdjacentSide

=

113

7

Solution(i):

(1+cosθ)(1−cosθ)

(1+sinθ)(1−sinθ)

We have, a

2

−b

2

=(a+b)(a−b)

Similarly,

(1−sin

2

θ)=(1+sinθ)(1−sinθ)

(1−cos

2

θ)=(1+cosθ)(1−cosθ)

Therefore,

(1+cosθ)(1−cosθ)

(1+sinθ)(1−sinθ)

=

(1−cos

2

θ)

(1−sin

2

θ)

=

(1−(

113

7

)

2

)

(1−(

113

8

)

2

)

=

(113−49)

(113−64)

=

64

49

Solution(ii):

Given,

cotθ=

8

7

cot

2

θ=(

8

7

)

2

=

64

49

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