Prove (cosec theta - cot theta)^2 | Exercise 8.4 Q5 part (i) | Important

Exercise 8.4 question 5 class 10

Prove:
〖(cosecθ-cotθ)〗^2=(1-cosθ)/(1+cosθ)
or
Prove that cosec θ - cot θ square = 1 - cos θ by 1 + cosθ

Hint 🗒️
1. Express cosec θ - cot θ into cos θ and sin θ
2. Using (a-b) whole square = a square + b square - 2ab, simplify the expression
3. Remember to use
1- sin^2 θ = cos^2 θ

Remember 💡
Trigonometric identities:
cos^2 A + sin^2 A = 1
1 + tan^2 A = sec^2 A
cot^2 A + 1 = cosec^2A

Note📝
The above question is taken from NCERT book Ch-8 exercise 8.4 question 5 part 1 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👩‍🏫:
Choose the correct option. Justify your choice.
(i) 9 sec² A – 9 tan² A = ……
(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ………..
(iii) (sec A + tan A) (1 – sin A) = ………….
(iv) 1+tan²A/1+cot²A = ………..

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