Question

Question 2 Write all the other trigonometric ratios of ∠A in terms of sec A.

Class 10 - Math - Introduction to Trigonometry Page 193

Answer 1

An equation involving trigonometric ratios of an angle is called a trigonometric identity. This is true for all angles A such that 0°≤A≤90°.

Some identities are:
1) cos² A + sin²A = 1

2) sec² A - tan² A = 1.

3) cosec² A - cot² A = 1.
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We know that,
sec A = 1/cos A
⇒ cos A = 1/sec A

cos²A + sin²A = 1
⇒  sin²A = 1 – cos²A
⇒  sin²A = 1 – (1/sec²A)                          (cosA= 1/secA)
⇒  sin²A = (sec²A-1)/sec²A

⇒sinA = √((sec²A-1)/sec²A)

⇒sinA = √(sec²A-1) ÷ (secA)............................(i)

sin A = 1/cosec A
⇒ cosec A = 1/sin A

⇒cosecA= secA ÷√sec²A-1                 (from eq i)

Now,
sec²A – tan²A = 1
⇒ tan²A = sec²A + 1

⇒tanA = √sec²A + 1.....................................(ii)

tan A = 1/cot A
⇒ cot A = 1/tan A

⇒cotA  = 1/√sec²A + 1                  (from eq ii)

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Hope this will help you..

Answer 2

Step-by-step explanation:

This is the full explanation of this sum..

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