Show that cosec square ø - tan square (90-ø) = sin square ø +sin square (90-ø)
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Cosec²∅ - tan²(90-∅) = LHS
1/sin²∅ - cot²∅
1/sin²∅ - cos²∅/sin²∅
1-cos²∅/sin²∅
sin²∅ / sin²∅
1
RHS = sin²∅ + sin²(90-∅)
sin²∅ + cos²∅
1
hence LHS = RHS
1/sin²∅ - cot²∅
1/sin²∅ - cos²∅/sin²∅
1-cos²∅/sin²∅
sin²∅ / sin²∅
1
RHS = sin²∅ + sin²(90-∅)
sin²∅ + cos²∅
1
hence LHS = RHS
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