Prove (cos A/1+sin A)+ (1+sin A/cos A)=2 sec A | Exercise 8.4 Q5 part(ii)

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Exercise 8.4 question 5 part II class 10
Prove:
cos ⁡A/(1+sin⁡A )+(1+sin⁡A)/cos⁡ A =2 sec ⁡A
or
cos A by 1+sin A + 1+sin A by cos A = 2 sec A

Hint 💡
1. Take the LCM of (1+sin A) and cos A
2. Use algebraic identity (a+b)^2
3. Use trigonometric identity
cos^2 A + sin^2 A = 1
4. Remember the relation cos A = 1/sec A

Trigonometric identity:
cos^2 A + sin^2 A = 1
1 + tan^2 A = sec^2 A
cot^2A + 1 = cosec^2A

Algebraic Identity
(a+b)^2 = a^2 + b^2 + 2ab
a^2 - b^2 = (a-b)(a+b)

Note📝
The above question is taken from NCERT book Ch-8 exercise 8.4 question 5 part 2 Trigonometry.

Read it 📖
Identity:
An equation is called an identity when it is true for all values of the variables involved in it.

Trigonometric identity :
Similarly, an equation involving trigonometric ratios of an angle is called a trigonometric identity, if it is true for all values of the angle(s) involved.

Practice👩‍🏫:
Prove:
(cosecθ-cotθ)^2=(1-cosθ)/(1+cosθ)

Trigonometric identities

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Real Numbers

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