Write all the other trigonometric ratios of ∠A in terms of sec A

Solution:

We will use the basic trigonometric identities and properties of the trigonometric ratios to solve the problem.

sin² A + cos² A = 1

cosec² A = 1 + cot² A

sec² A = 1 + tan² A

We know that,

cos A = 1/sec A .....Equation (1)

Also,

sin² A + cos² A = 1 (trigonometric identity)

sin² A = 1 - cos² A (By transposing)

Using value of cos A from Equation (1) and simplifying further

sin A = √1 - (1 / sec A)²

= √(sec² A - 1) / sec² A

= √(sec² A - 1) / sec A ....Equation (2)

tan² A + 1 = sec² A (Trigonometric identity)

tan² A = sec² A - 1 (By transposing)

tan A = √(sec² A - 1) ... Equation (3)

cot A = cosA/sinA

= (1/sec A) / [√(sec² A - 1)/sec A] .....(By substituting the values from Equations (1) and (2))

= 1 / √(sec² A - 1)

cosec A = 1/sin A

= sec A / √(sec² A - 1) (By substituting from Equation (2) and simplifying)

☛ Check: NCERT Solutions for Class 10 Maths Chapter 8

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Video Solution:

Write all the other trigonometric ratios of ∠A in terms of sec A.

Maths NCERT Solutions Class 10  Chapter 8 Exercise 8.4 Question 2

Summary:

All the other trigonometric ratios of ∠A in terms of sec A are cos A = 1/sec A, sin A = √(sec²A − 1)/sec A, tan A = √(sec²A − 1), cot A = 1/√(sec²A − 1), and cosec A = sec A/√(sec²A − 1).

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