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Question
A triangle ABC is right-angled at B; find the value of `(sec "A". sin "C" - tan "A". tan "C")/sin "B"`.
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Solution
Since Δ ABC is a right angled triangle, right angled at B,
A + C = 90°
∴ `(sec "A".sin "C" - tan "A". tan "C")/sin "B"`
= `(sec "A"(90° - "C")sin "C" - tan(90° - "C")tan "C")/(sin 90°)`
= `("cosec" "C" sin "C" - cot "C" tan "C")/(1)`
= `(1)/sin "C" xx sin "C" - (1)/tan "C" xx tan "C"`
= 1 - 1
= 0
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