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CBSE Class 12-science Answered

Which is the correct option? Let 
begin mathsize 20px style P equals open curly brackets theta colon sin theta minus cos theta equals square root of 2 cos theta close curly brackets space a n d space Q equals open curly brackets theta colon sin theta plus cos theta equals square root of 2 sin theta close curly brackets b e space t w o space s e t s. T h e n open parentheses a close parentheses P subset of Q space a n d space Q minus P space n o t space e q u a l space t o empty set open parentheses b close parentheses Q ⊄ P open parentheses c close parentheses P ⊄ Q open parentheses d close parentheses P equals Q end style
Asked by sunil2791 | 11 Jun, 2017, 11:31: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight P equals left curly bracket straight theta colon sinθ minus cosθ equals square root of 2 cosθ right curly bracket straight Q equals left curly bracket straight theta colon sinθ plus cosθ equals square root of 2 sinθ right curly bracket Consider comma space sinθ minus cosθ equals square root of 2 cosθ rightwards double arrow cos open parentheses straight pi over 2 minus straight theta close parentheses minus cosθ equals square root of 2 cosθ rightwards double arrow 2 sin open parentheses fraction numerator straight pi over 2 minus straight theta plus straight theta over denominator 2 end fraction close parentheses sin open parentheses fraction numerator straight theta minus straight pi over 2 plus straight theta over denominator 2 end fraction close parentheses equals square root of 2 cosθ rightwards double arrow 2 sin straight pi over 4 sin open parentheses straight theta minus straight pi over 4 close parentheses equals square root of 2 cosθ rightwards double arrow 2 cross times fraction numerator 1 over denominator square root of 2 end fraction sin open parentheses straight theta minus straight pi over 4 close parentheses equals square root of 2 cosθ rightwards double arrow sin open parentheses straight theta minus straight pi over 4 close parentheses equals cosθ rightwards double arrow sin open parentheses straight theta minus straight pi over 4 close parentheses equals sin open parentheses straight pi over 2 minus straight theta close parentheses rightwards double arrow straight theta minus straight pi over 4 equals straight pi over 2 minus straight theta rightwards double arrow straight theta equals fraction numerator 3 straight pi over denominator 8 end fraction.......................... left parenthesis straight i right parenthesis Similarly comma sinθ plus cosθ equals square root of 2 sinθ sinθ plus sin open parentheses straight pi over 2 minus straight theta close parentheses equals square root of 2 sinθ 2 sin open parentheses fraction numerator straight theta plus straight pi over 2 minus straight theta over denominator 2 end fraction close parentheses cos open parentheses fraction numerator straight theta minus straight pi over 2 plus straight theta over denominator 2 end fraction close parentheses equals square root of 2 sinθ 2 sin straight pi over 4 cos open parentheses straight theta minus straight pi over 4 close parentheses equals square root of 2 sinθ 2 cross times fraction numerator 1 over denominator square root of 2 end fraction cos open parentheses straight theta minus straight pi over 4 close parentheses equals square root of 2 sinθ cos open parentheses straight theta minus straight pi over 4 close parentheses equals cos open parentheses straight pi over 2 minus straight theta close parentheses straight theta minus straight pi over 4 equals straight pi over 2 minus straight theta 2 straight theta equals straight pi over 2 plus straight pi over 4 straight theta equals fraction numerator 3 straight pi over denominator 8 end fraction....................... left parenthesis ii right parenthesis From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis straight P equals straight Q end style
Answered by Sneha shidid | 12 Jun, 2017, 09:30: AM

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CBSE 12-science - Maths
2+2=?
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CBSE 12-science - Maths
In R - {-1}, there is a binary operation '*' defined by a*b = a+b - ab, for all a,b belongs to R - {-1}. Is R - {-1} group?
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CBSE 12-science - Maths
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CBSE 12-science - Maths
 Consider the binary operation * on the set {1, 2, 3, 4, 5} defined by a*b=HCF of a andb. Write the operation table of the operation *. Is * commutative? Justify. Also, compute: (a) (2*3)*5 (b) (2*3)*(4*5). 
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CBSE 12-science - Maths
 Show that the binary operation * on A = R – {-1} defined as a*b = a + b + ab for all a,b belongs to A is commutative and associative on A. also find the identity element of  * in A and prove that every element of A in invertible mention each and every formula and minute details
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CBSE 12-science - Maths
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CBSE 12-science - Maths
A binary operation is defined by x * y = 2x – 3y. Find *(3, 2).
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CBSE 12-science - Maths
A binary operation is defined by a * b = ab/2. Is the binary operation commutative?
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
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CBSE 12-science - Maths
A binary operation defined by a * b = ab. Is the binary operation associative?
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CBSE 12-science - Maths
For the binary operation * defined by a * b = a + b + 1. Find the identity element for operation *.
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