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प्रश्न
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
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उत्तर
`cot[sin^-1 3/5 + sin^-1 4/5]`
= `cot [sin^-1 (3/5 sqrt(1 - (4/5)^2) + 4/5 sqrt(1 - (3/5)^2))]`
= `cot[sin^-1 (3/5 sqrt(1 - 16/25) + 4/5 sqrt(1 - 9/25))]`
= `cot [sin^-1 (3/5 sqrt(9/25) + 4/5 sqrt(16/25))]`
= `cot [sin^-1 (3/5 xx 3/5 + 4/5 xx 4/5)]`
= `cot[sin^-1 (9/25 + 16/25)]`
= `cot[sin^-1 (25/25)]`
= `cot [sin^-1(1)]`
= `cot pi/2`
= 0
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