Question

Example: Given sec θ=4, find the values of the other five trigonometric functions of θ
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Answer 1

Answer:

1/4

Step-by-step explanation:

sec theta=4

1/cos theta=4,cos theta=1/4

Answer 2

Answer:

if k (sec α+ tan α)(sec β+ tan β)(sec γ+tan γ) (sec α-tan α)(sec β-tan β)(sec γ-tan γ).then k=secα=secβsecγ+tanβtanγ⟹tanβtanγ=secα−secβsecγ

squaring on both sides

tan

2

βtan

2

γ=sec

2

α+sec

2

βsec

2

γ−2secαsecβsecγ⟹(sec

2

β−1)tan

2

γ

=sec

2

α+sec

2

βsec

2

γ−2secαsecβsecγ

(sec

2

γ−tan

2

γ)sec

2

β−(2secαsecγ)secβ+(sec

2

α+tan

2

γ)=0

⟹sec

2

β−(2secαsecγ)secβ+(sec

2

α+tan

2

γ)=0

this is in the form of ax

2

+bx+c=0 whose roots are

2a

−b±

b

2

−4ac

⟹secβ=

2(1)

2secαsecγ±

4sec

2

αsec

2

γ−4(tan

2

γ+sec

2

α)

=secαsecγ±

sec

2

α(sec

2

γ−1)−tan

2

γ

=secαsecγ±

tan

2

γ(sec

2

α−1)

=secαsecγ±tanαtanγ