Exercise 8.4 question 5 part viii class 10
Prove:
〖(sinA+cosecA)^2+〖(cosA+secA)〗^2=7+〖tan 〗^2A+〖cot〗^2 A
or
Prove that sin A + cosec A whole square + cos A + cosec A whole square equal to 7 + tan square A + cos square A
Strategy🧠:
Use algebraic identity (a+b)^2 = a^2 + b^2 + 2ab
Remember,
sin A x cosec A = 1
cos A x sec A =1
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 8 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.
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