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Ex. 6Show that cos 1+sin1sin-11365 |
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Answer» cos¯¹ 12/13 + sin¯¹ 3/5 = sin¯¹ 56/65Taking LHS :sin¯¹ 5/13 + sin¯¹ 3/5 Using the formula, sin¯¹x + sin¯¹y = sin¯¹ ( x√1-y² + y√1-x² )= sin¯¹ ( 5/13 √1-9/25 + 3 √1-25/169)= sin¯¹ ( 5/13 × 4/5 + 3/5 × 12/13)= sin¯¹ (30 + 36 / 65)= sin¯¹ (56/ 65)= RHS Hence proved |
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