What is tan(arcsin((h-T)/W)) ?

The solution to tan(arcsin((h-T)/W)) is ((h-T)sqrt(W^2-h^2+2hT-T^2))/(W^2-h^2+2hT-T^2)

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simplify tan(arcsin((h-T)/W))

simplify

tan (arcsin (\frac{h - T}{W}))

\frac{( h - T ) W ^{2} - h ^{2} + 2 h T - T ^{2}}{W ^{2} - h ^{2} + 2 h T - T ^{2}}

Solution steps

tan (arcsin (\frac{h - T}{W}))

Use the following identity:

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}}

= \frac{( \frac{h - T}{W} ) 1 - ( \frac{h - T}{W} ) ^{2}}{1 - ( \frac{h - T}{W} ) ^{2}}

Simplify

= \frac{( h - T ) W ^{2} - h ^{2} + 2 h T - T ^{2}}{W ^{2} - h ^{2} + 2 h T - T ^{2}}

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What is tan(arcsin((h-T)/W)) ?
The solution to tan(arcsin((h-T)/W)) is ((h-T)sqrt(W^2-h^2+2hT-T^2))/(W^2-h^2+2hT-T^2)