Question
Download Solution PDFLet PQR be a right angled triangle, right-angled at R. Let PQ = 29 cm, QR = 21 cm and ∠Q = θ. Find the value of cos2 θ – sin2 θ.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Let PQR be a right-angled triangle, right-angled at R.
PQ = 29 cm, QR = 21 cm, and ∠Q = θ.
Formula used:
cos² θ - sin² θ = cos 2θ
Calculations:
In Triangle PQR using the Pythagorean theorem:
⇒ PR² = PQ² - QR²
⇒ PR² = 29² - 21²
⇒ PR² = 841 - 441
⇒ PR = 20 cm
cos θ = QR / PQ = 21 / 29
sin θ = PR / PQ = 20 / 29
Next, we use the identity for cos² θ - sin² θ:
⇒ cos² θ - sin² θ = (cos θ + sin θ) × (cos θ - sin θ)
⇒ cos² θ - sin² θ = (21/29)² - (20/29)²
⇒ cos² θ - sin² θ = (441/841) - (400/841)
⇒ cos² θ - sin² θ = (441 - 400) / 841 = 41 / 841
∴ The correct answer is option (1).
Last updated on Jul 22, 2025
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