Question

if sec0+tan0=k, then prove sec0=k2-1/k2+1​

Answer 1

Step-by-step explanation:

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Class 11

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>>If sectheta + tantheta = k ...

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If secθ+tanθ=k, then cosθ= _______.

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Solution

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Correct option is

B

k

2

+1

2k

Given secθ+tanθ=k

As we know that

sec

2

θ−tan

2

θ=1

⟹(secθ+tanθ)(secθ−tanθ)=1

⟹secθ−tanθ=

k

1

⟹secθ=

2

k+

k

1

=

2k

1+k

2

⟹cosθ=

k

2

+1

2k

Answer 2

Step-by-step explanation:

Given:

secФ + tanФ = k

To prove:

secФ = $\frac{k^{2} +1}{2k}$

Proof:

secФ + tanФ = k            ...1

We have identity,

sec^{2}Ф -tan^{2}Ф =1

(secФ + tanФ)(secФ-tanФ) = 1

k(secФ-tanФ)=1

(secФ-tanФ)=1/k          ....2

Adding equations 1 and 2

secФ + tanФ = k

secФ - tanФ =1/k    

2secФ = k+1/k

secФ = $\frac{k^{2} +1}{2k}$