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If. tan¶+sin¶ = M. tan¶-sin¶ = N. Prove M sq. - N sq.= 4√m√n |
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Answer» M² - N²=(√tan² θ sin² θ).M² - N²= √ tan ² θ(1-cos² θ).=4 √tan ²θ- tan ²θ cos ² θ.= 4 √tan² θ - sin ² θ.=4 √ ( tan θ + sin θ) ( tan θ- sin θ ).=4 √mn.PROVED. Tan θ + sin θ= M. Tan θ - sin θ= N.M² - N² = (Tan θ + sin θ)² - (Tan θ - sin θ)². M² - N²=(Tan ²θ + sin ²θ + 2 tan θ sin θ )-(Tan ²θ + sin ²θ - 2 tan θ sin θ ).M² - N²=Tan ²θ + sin ²θ + 2 tan θ sin θ-Tan ²θ - sin ²θ +2 tan θ sin θ.M² - N²=4 tan θ sinθ.M² - N²= This is in rd sharma Solve LHS you will got tan¶sin¶ Then solve RHS you will got tan¶sin¶ Hence proved Solve RHS and LHS seperately |
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