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Write all the other trigonometric ratio of angle a in terms of sec a

sec2A−tan2A=1
⇒tan2A=sec2A−1
⇒tanA=√sec2A−1−−−−−−−−     (1)
 cos A = 1 / secA −−−−−−−−     (2)
sin2A+cos2A=1
⇒sin2A=1−cos2A
Putting (2) in the above equation we get
sin2A=1−(1 / secA)2=sec2A−1 / sec2A
⇒sinA=√sec2A−1 / secA             −−−−−−−−           (3)
We know that  cosecA=1 / sinA
Putting (3) in the above equation, we get
cosecA=secA / √sec2A−1         (4)
We know that  cotA=1 / tanA
Putting (1) in the above equation, we get
cotA=1/ √sec2A−1                    (5)
(1), (2), (3), (4) and (5) shows all the other trigonometric ratios of ∠A in terms of sec A.

 


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