Question

if sec ∝+tan ∝=p then find the value of cos ∝ and cot ∝

Answer 1

Answer:

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Answer 2

Answer

secθ+tanθ=p ... (1)

secθ−tanθ=

p

1

... (2)

(1) + (2)

⇒2secθ=p+

p

1

⇒secθ=

2

1

(p+

p

1

)

⇒

cosθ

1

=

2

1

(p+

p

1

)=

2

1

(

p

p

2

+1

)

⇒cosθ=(

p

2

+1

2p

)

(1) - (2)

⇒2tanθ=p−

p

1

⇒tanθ=

2

1

(p−

p

1

)

⇒

cosθ

sinθ

=

2

1

(p−

p

1

)

⇒sinθ=[

2

1

(p+

p

1

)]cosθ

⇒sinθ=

p+

p

1

p−

p

1

=

p

2

+1

p

2

−1

⇒cosecθ=

p

2

−1

p

2

+1