Proof of Trigonometric Identities Class 10

List of All Trigonometric Identities Class 10

In this section we will prove trigonometric identities class 10 that are mentioned above.

By Pythagoras theorem

PR² = PQ² + QR² – – -(1)

Proof of sin²θ + cos²θ = 1

Dividing equation (1) by PR²

1 = PQ²/PR² + QR²/PR²

⇒ 1 = (PQ/PR)² + (QR/PR)² – – -(2)

In right-angled triangle PQR

PQ/PR = sin θ

and QR/PR = cos θ

Put value of PQ/PR and QR/PR in equation (2), we get

sin²θ + cos²θ = 1

Hence proved.

Proof of 1 + tan²θ = sec²θ

Dividing equation (1) by QR²

PR²/QR²= PQ²/QR² + 1

⇒ (PR/QR)² = (PQ/QR)² + 1 – – -(3)

In right-angled triangle PQR

PR/QR = sec θ

and PQ/QR = tan θ

Put value of PR/QR and PQ/QR in equation (3), we get

1 + tan²θ = sec²θ

Hence proved.

Proof of 1 + cot²θ = cosec²θ

Dividing equation (1) by PQ²

(PR²/PQ²) = 1 + (QR²/PQ²)

(PR/PQ)² = 1 + (QR/PQ)² – – – (4)

In right-angled triangle PQR

PR/PQ = cosec θ

and QR/PQ = cot θ

Put value of PR/PQ and QR/PQ in equation (4), we get

1 + cot²θ = cosec²θ

Hence proved.

Trigonometric Identities Class 10

Trigonometric Identities are the rules that are followed by the Trigonometric Ratios. Trigonometric Identities and ratios are the fundamentals of trigonometry. Trigonometry is used in various fields for different calculations. The trigonometric identities class 10 gives the connection between the different trigonometric ratios. This article covers trigonometric identities class 10 in addition to their proofs.

This article will be extremely helpful for class 10 students for their exams. Also, we will solve some examples of trigonometric identities Class 10. Let’s discuss the topic of Trigonometric Identities Class 10 in depth.

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