Question

If 1 + x square whole root sin theta = x, prove that tan square theta + cot square theta = x square + 1/x square.
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Answer 1

Answer:

We are required to prove ( 1 - cos^{2}1−cos 2

We are required to prove ( 1 - cos^{2}1−cos 2 ∅) sec^{2}sec 2 ∅ = tan∅

∅ = tan∅Solution :

∅ = tan∅Solution :LHS = ( 1 - cos^{2}1−cos

∅ = tan∅Solution :LHS = ( 1 - cos^{2}1−cos 2 ∅) sec^{2}sec 2 ∅

∅ = sin^{2}sin 2∅ sec^{2}sec 2∅ (as cos^{2}cos 2 ∅ + sin^{2}sin 2∅ = 1)

∅ sec^{2}sec 2∅ (as cos^{2}cos 2 ∅ + sin^{2}sin 2∅ = 1) = sin^{2}sin 2 ∅/cos^{2}cos 2 ∅

∅ sec^{2}sec 2∅ (as cos^{2}cos 2 ∅ + sin^{2}sin 2∅ = 1) = sin^{2}sin 2 ∅/cos^{2}cos 2 ∅ = tan^{2}tan 2 ∅

∅RHS = tan^{2}tan 2∅

∅RHS = tan^{2}tan 2∅∴ LHS = RHS