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Question : 74 of 160
Marks:
+1,
-0
Solution:
Consider the expression,
∫[| cot‌x‌cos(x+α)+sin‌x‌sin(x+α) |
| sin‌x‌sin(x+α) |
]dx =∫[| cos‌α |
| sin‌x‌sin(x+α) |
]dx =‌∫[| sin‌α |
| sin‌x‌sin(x+α) |
]dx =cos‌α‌∫[| sin(x+α)−x |
| sin‌x‌sin(x+α) |
]dx Further simplify the above,
∫[| cot‌x‌cos(x+α)+sin‌x‌sin(x+α) |
| sin‌x‌sin(x+α) |
]dx =cot‌α‌∫[cot‌x−cot(x+α)]dx =cot‌α[log|sin‌x|−log| sin(x+α)|]+c Further simplify the above,
∫[| cot‌x‌cos(x+α)+sin‌x‌sin(x+α) |
| sin‌x‌sin(x+α) |
]dx =cot‌α‌log(||)+c
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