Prove (sin θ-2 sin^3 θ)/ (2 cos^3 θ - cos θ) = tan θ | Exercise 8.4 Q5 part vii

Exercise 8.4 question 5 part vii class 10

Strategy🧠:
Take sin θ and cos θ common from numerator and denominator respectively
Use Trigonometric Identity

Prove:
(sinθ-2〖sin〗^3 θ)/(2〖cos〗^3 θ-cosθ)=tanθ
Hint 💡 :
Trigonometric identity:
cos2 A + sin2 A = 1
1 + tan2 A = sec2 A
cot2 A + 1 = cosec2A

Algebraic Identity
(a+b)^2 = a^2 + b^2 + 2ab
(a+b)^3 = (a+b)(a^2 -ab + b^2)
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 7 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👩‍🏫:
√((1+sin⁡A)/(1-sin⁡A ))=sec ⁡A + tan ⁡A
Prove √(1+sin A)/(1-sin A) = sec A + ...

Trigonometric identities
Prove trigonometric identities class ...

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