PW tenthies study material

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1. Prove that (√3 + 1) (3 – cot 30°) = tan360° – 2 sin 60°. 2. Prove that (sin4θ – cos4θ +1) cosec2θ = 2 3. If tan(A + B) = √3 and tan(A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B, find A and B. 4. If A, B and C are interior angles of a triangle ABC, show that sin (B + C/2) = cos A/2. 5. If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A. 6. If tan θ + sec θ = l, prove that sec θ = (l2 + 1)/2l. 7. Prove that (cos A – sin A + 1)/ (cos A + sin A – 1) = cosec A + cot A, using the identity cosec2A = 1 + cot2A. 8. Prove that: (cosec A – sin A)(sec A – cos A) = 1/(tan A + cot A) [Hint: Simplify LHS and RHS separately] 9. If a sin θ + b cos θ = c, prove that a cosθ – b sinθ = √(a2 + b2 – c2). Solve all these question till 5 P.M. Let's see how you are prepare for your board examinations.

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