Question
If sin(x + y) = 1 and sin(x - y) = (1/2), then what is
the value of sinx cosx + 2sin2y + cos2y?Solution
We have given, sin(x + y) = 1 and sin(x - y) = 1/2 So, sin(x + y) = 1 Or, sin(x + y) = sin90° Or, (x + y) = 90° ......(i) Again, sin(x - y) = 1/2 Or, sin(x - y) = sin30° Or, (x - y) = 30° ......(ii) By adding (i) and (ii) we get, 2x = 120° Or, x = 60° Putting the value of 'x' in the eq (i) we get, y = 30° Now, sinx cosx + 2sin2y + cos2y = sin60° X cos60° + 2 X sin230° + cos230° = = (1/2) X (√3/2) + 2 X (1/2)2 + (√3/2)2 = (1/2) X (√3/2) + 2 X (1/4) + (3/4) = (√3/4) + (1/2) + (3/4) = {(√3 + 2 + 3)/4} = {(√3 + 5)/4}
What recognition did UNESCO recently award to West Bengal?
Which organization is organizing the Aadi Mahotsav 2024, inaugurated by the President of India?
What is the proposed new wage ceiling for EPF contributions under the government’s revision?
What event did Prime Minister Shri Narendra Modi address via video message?
What is the total number of Pro Bono advocates registered under the Nyaya Bandhu programme as of January 31, 2024?
What is the main focus of the India-Israel Business Forum and CEO Forum scheduled for February 11, 2025?
Which organization recently launched an Integrated Tribal Development Programme (ITBP) in the Kulathupuzha grama panchayat, Kerala?
How much has the Adani Group pledged to invest in Chhattisgarh across various sectors?
What was the significance of Donald Trump renaming the Gulf of Mexico as the ‘Gulf of America’?
What was Andhra Pradesh’s score in the “State of India’s Environment 2025 in Figures” report?