Step-by-step explanation:
We know that 1+tan
2
θ=sec
θ
⇒tan
θ−1
⇒tanθ=
sec
⇒
cotθschool
1
=
⇒cotθ=
Answer:
The value of sinθ in terms of secθ will be [tex]\frac{\sqrt{sec\theta^{2}-1} }{sec\theta}[/tex]
The value of cotθ in terms of secθ will be equal to [tex]\frac{1}{\sqrt{sec^{2}\theta-1}}[/tex].
We are going to use two relations to get these values:
We know
[tex]sin^{2}\theta+cos^{2}\theta=1[/tex]
[tex]sin^{2}\theta=1-cos^{2}\theta[/tex]
[tex]sin^{2}\theta=1-\frac{1}{sec^{2}\theta}[/tex]
[tex]sin\theta=\sqrt{\frac{sec^{2}\theta-1}{{sec^{2}\theta} } }[/tex]
∴ [tex]sin\theta=\frac{\sqrt{sec\theta^{2}-1} }{sec\theta}[/tex]
Again [tex]sec^{2}\theta-tan^{2}\theta=1[/tex]
[tex]tan^{2}\theta=sec^{2}\theta-1[/tex]
We get [tex]tan\theta=\sqrt{sec^{2}\theta-1}[/tex]
[tex]cot\theta=\frac{1}{\sqrt{sec^{2}\theta-1}}[/tex]
Hence we get the values of sinθ and cot θ in terms of secθ.
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Answers & Comments
Step-by-step explanation:
We know that 1+tan
2
θ=sec
2
θ
⇒tan
2
θ=sec
2
θ−1
⇒tanθ=
sec
2
θ−1
⇒
cotθschool
1
=
sec
2
θ−1
⇒cotθ=
sec
2
θ−1
1
Answer:
The value of sinθ in terms of secθ will be [tex]\frac{\sqrt{sec\theta^{2}-1} }{sec\theta}[/tex]
The value of cotθ in terms of secθ will be equal to [tex]\frac{1}{\sqrt{sec^{2}\theta-1}}[/tex].
Step-by-step explanation:
We are going to use two relations to get these values:
We know
[tex]sin^{2}\theta+cos^{2}\theta=1[/tex]
[tex]sin^{2}\theta=1-cos^{2}\theta[/tex]
[tex]sin^{2}\theta=1-\frac{1}{sec^{2}\theta}[/tex]
[tex]sin\theta=\sqrt{\frac{sec^{2}\theta-1}{{sec^{2}\theta} } }[/tex]
∴ [tex]sin\theta=\frac{\sqrt{sec\theta^{2}-1} }{sec\theta}[/tex]
Again [tex]sec^{2}\theta-tan^{2}\theta=1[/tex]
[tex]tan^{2}\theta=sec^{2}\theta-1[/tex]
We get [tex]tan\theta=\sqrt{sec^{2}\theta-1}[/tex]
[tex]cot\theta=\frac{1}{\sqrt{sec^{2}\theta-1}}[/tex]
Hence we get the values of sinθ and cot θ in terms of secθ.