Question
Suppose 140sin²X + 124cos²X = 136 and 184sin²Y +
200cos²Y = 196, then determine the value of 18cosec²Xsec²Y.Solution
ATQ,
Since, 140sin²X + 124cos²X = 136
So, 124(sin²X + cos²X) + 16sin²X = 136
Or, 16sin²X = 12
Or, sin²X = 12/16 = 3/4
Or, sinX = √3/2
So, X = 60⁰
Similarly, Y = 30⁰
So, 18cosec²Xsec²Y = 18 × 4/3 × 4/3 = 32
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