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Question

If sinA+sinB+sinC+sinD=4 then find the value of sinA×sinB×sinC×sinD.


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Solution

Step 1: Compare the range of LHS and RHS.

Range of sinxx is -1,1

-1sinA1-1sinB1-1sinC1-1sinD1

Adding all four equations

-4sinA+sinB+sinC+sinD4

For sinA+sinB+sinC+sinDto be equal to 4, sinA=sinB=sinC=sinD=1

Step 2: Calculate the given expression.

Since sinA=sinB=sinC=sinD=1

sinA×sinB×sinC×sinD=14=1

Hence, value of sinA×sinB×sinC×sinD is 1.


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