Class 11 Exam > Class 11 Questions > Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?
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Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?
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Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?
Solution:
Given expression is (Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4
Step 1: Simplify the numerator
First, we will simplify the numerator
(Sin¤ icos¤)^2 = [(Sin¤)^2 (cos¤)^2] = (Sin¤)^2 (1 - Sin^2¤) = (Sin^3¤ - Sin¤)
(1 icot¤)^3 = (1 icot¤)^2 (1 icot¤) = (1 - 2icot¤ - icot^2¤) (1 icot¤) = (1 - icot¤ - icot^2¤) = (1 - cos¤ - isin¤)
Now, we can substitute these values in the expression:
(Sin^3¤ - Sin¤) [(1 - cos¤ - isin¤)]^3
Step 2: Simplify the denominator
Next, we will simplify the denominator
(1 i tan¤)^4 = (1 + itan¤)^4 (1 - itan¤)^4 = [(1 - tan^2¤) + 2itan¤]^4 [(1 - tan^2¤) - 2itan¤]^4 = [1 - 4tan^2¤ - 6itan¤ - 4tan^4¤ - i8tan^3¤]^4
Step 3: Combine the terms
Now we can substitute the above values in the expression and simplify:
(Sin^3¤ - Sin¤) [(1 - cos¤ - isin¤)]^3 / [1 - 4tan^2¤ - 6itan¤ - 4tan^4¤ - i8tan^3¤]^4
Step 4: Further simplification
Finally, we can simplify the above expression by multiplying the numerator and the denominator by the conjugate of the denominator:
(Sin^3¤ - Sin¤) [(1 - cos¤ - isin¤)]^3 [(1 + 4tan^2¤ + 6itan¤ + 4tan^4¤ + i8tan^3¤)]^4 / [(1 + 4tan^2¤)^8 + 64tan^6¤]^2
Therefore, the simplified expression is (Sin^3¤ - Sin¤) [(1 - cos¤ - isin¤)]^3 [(1 + 4tan^2¤ + 6itan¤ + 4tan^4¤ + i8tan^3¤)]^4 / [(1 + 4tan^2¤)^8 + 64tan^6¤]^2
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Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?
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Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?
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Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?.
Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.(Sin¤ icos¤)^2 (1 icot¤)^3/(1 i tan¤)^4?.
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