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Question
A triangle ABC is right angles at B; find the value of`(secA.cosecC - tanA.cotC)/sinB`
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Solution
Since, ABC is a right angled triangle, right angled at B.
So, A + C = 90°
`(secA.cosecC - tanA.cotC)/sinB`
= `(sec(90^circ - C).cosecC - tan(90^circ - C).cotC)/sin90^circ`
= `(cosecC.cosecC - cotC.cotC)/1`
= 1 ...[∵ cosec2θ – cot2θ = 1]
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