10th trigonometry test paper

Q. 1. If sin A = ¾ . Find cos A and tan A.

Q. 2. In triangle ABC, right angle At B. if tan A = 1/√3 find the values of the following

sin A cos C + cos A sin C

cos A cos C – sin A sin C

Q. 3. If tan (A+B) = √3 and tan (A – B) = 1/√3. Find the value of A and B.

Q. 4. If tan 2A = cot (A – 180), where 2A is an acute angle. Find the value of A.

Q. 5. If A,B and C are interior angles of the triangle ABC, then show that

Sin {(B+C)/2} = cos A/2

Q. 6. prove the following identity

(cosec A – cot A) = (1- cos A) /(1+ cos A)

Q. 7. (sin A + cosecA) 2 + (cos A + sec A) 2 = 7 + tan 2A + cot 2A .prove it.

Q. 8. ( cosec A – sin A ) ( sec A – cos A) = 1/ ( tan A + cot A)

Q. 9. prove that cos⁴A -– cos²A = sin⁴A – - sin²A

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