CBSE - Mathematics - Introduction to Trigonometry

We know that sec²A−tan²A=1

⇒tan²A=sec²A−1

⇒tan²A=sec²A−1

⇒tanA = √ sec²A−1−−−−−−−−    (1)

We know that cos A = 1 / secA      (2)

We know that sin²A+cos²A=1

⇒sin2A=1−cos2A

Putting (2) in the above equation we get

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.