6.If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
Let us consider two right angle triangles right angled at Q and S respectively. Now,
But cos A = cos B (given) ∴
Let In ΔRAS, Using Pythagoras theorem, we have In APBQ, Using Pythagoras theorem, we have So, Comparing (i) and (ii), we get So, by using SSS similar condition ∴
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7.
If cot θ = evaluate:
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Short Answer Type
8.If 3 cot A = 4, check whether or not.
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Long Answer Type
9.In triangle ABC, right angled at B, if find the value of : (i) sin A cos C + cos A sin C (ii) cos A .cos C - sin A.sin C.
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10.In ΔPQR, right angled at Q. PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.