Question

given cot theta=7/8then find 1+sin theta/cos theta
​

Answer 1

Step-by-step explanation:

cotθ=

8

7

BC

AB

=

8

7

∴AB=7,BC=8

In ⊥ΔABC,∠B=90

0

∴AC

2

=AB

2

+BC

2

=(7)

2

+(8)

2

=49+64

AC

2

=113

∴AC=

113

sinθ=

AC

BC

=

113

8

cosθ=

AC

AB

=

113

7

(i)

(1+cosθ)(1−cosθ)

(1+sinθ)(1−sinθ)

=

(1+

113

7

)(1−

113

7

)

(1+

113

8

)(1−

113

8

)

=

(1)

2

−(

113

7

)

2

(1)

2

−(

113

8

)

2

=

1−

113

49

1−

113

64

=

64

49

(ii) cotθ=

8

7

∴cot

2

θ=(

8

7

)

2

=

64

49

solution

Answer 2

Step-by-step explanation:

ATQ

$\cot(x) = \frac{7}{8} \\ \: to \: find \: 1 + \tan(x) \\ we \: know \: \ \cot(x) = \frac{1}{ \tan(x) } = > \tan(x = \frac{8}{7} ) \\ now \: \: 1 + \frac{8}{7} = \frac{15}{7}$

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