Usethe formulas and table given in this article wherever necessary. Q.1: In ABC, right-angled at B, AB=22 cm and BC=17 cm. Find: (a) sin A Cos B (b) tan A tan B. Q.2: If 12cot θ= 15, then find sec θ. Q.3: In Δ PQR, right-angled at Q, PR + QR = 30 cm and PQ = 10 cm. Determine the values of sin P, cos P and tan P.Let$ \sin^{-1}a=\theta_1, \quad \sin^{-1}b=\theta_2,\\ \sin(\theta_1+\theta_2)=\sin(\sin^{-1}a +\sin^{-1}b),\\ \sin(\theta_1+\theta_2)=\sin(\sin^{-1}a)·\cos(sin^{-1}b) +\sin(\sin^{-1}b)·\cos(sin^{-1}a),\\ \theta_1+\theta_2=\sin(\sin^{-1}a)·\cos(sin^{-1}b) +\sin(\sin^{-1}b)·\cos(sin^{-1}a),\\ \sin^{-1}a+\sin^{-1}b=\sin(\sin^{-1}a).cos(sin Theproduct-to-sum formulas can be helpful in solving integration problems involving the product of trigonometric ratios. Integrate \int \! \sin 3x \cos 4x \, \mathrm {d}x. ∫ sin3xcos4xdx. This problem may seem tough at first, but after using the product-to-sum trigonometric formula, this integral very quickly changes into a standard form.
Thesine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse: \sin=\frac {\text {opposite}} {\text {hypotenuse}} sin = hypotenuseopposite. Using this, we have the relations \sin (A)=\frac {a} {c} sin(A) = ca y \sin (B)=\frac {b} {c} sin(B) = cb in the triangle above.
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