Question

tell me the identities of trigonometry grade 10​

Answer 1

Step-by-step explanation:

Trigonometric Identities for Class 10

In class 10th, there are basically three trigonometric identities, which we learn in trigonometry chapter. They are:

Cos2 θ + Sin2 θ = 1

1 + Tan2 θ = Sec2 θ

1 + Cot2 θ = Cosec2 θ

Here, we will prove on trigonometric identity and will use it to prove the other two. Take an example of a right-angled triangle ΔABC.

In a right-angled triangle, by the Pythagorean theorem, we know,

(Perpendicular)2 + (Base)2 = (Hypotenuse)2

Therefore, in ΔABC, we have;

AB2 + BC2 = AC2 ….. (1)

Dividing equation (1) by AC2, we get,

AB2AC2 + BC2AC2 = AC2AC2

(ABAC)2 + (BCAC)2 = (ACAC)2

(Cosθ)2+(Sinθ)2 = 12

Cos2 θ + Sin2 θ = 1 …..(2)

If θ = 0, then,

Cos2 0 + Sin2 0 = 1

12 + 02 = 1

1 + 0 = 1

1 = 1

And if we put θ = 90,then

Cos2 90 + Sin2 90 = 1

02 + 12 = 1

0 + 1 = 1

1 = 1

For all angles, 0°≤ θ ≤ 90°, equation (2) is satisfied. Hence, equation (2) is a trigonometric identity.

Again, divide equation (1) by AB2, we get

AB2AB2 + BC2AB2 = AC2AB2

(ABAB)2 + (BCAB)2 = (ACAB)2

1 + Tan2 θ = Sec2 θ …..(3)

If θ = 0, then,

1 + tan20 = sec20

1 + 02 = 12

1 = 1

And if we put θ = 90,then

1 + tan290 = sec290

1 + ∞ = ∞

∞ = ∞

As you can see, the values of both sides are equal. Therefore, it proves that for all the values between 00 and 900, the equation (3) is satisfied. So, it is also a trigonometric identity