Using identities and algebra show that sec2theta sin2theta

Using identities and algebra show that sec^2(theta) - sin^2(theta) sec^2(theta) = 1. Using algebra and your knowledge of identities show that sec(A)/sin(A) - sin(A)/cos(A) = cot(A).

Solution

1) sec² -sin²sec²

=sec²(1-sin²)

=sec²*cos²........................(since sin²+cos²=1)

=(1_/cos²)*cos²

=1

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2)[secA_/sinA]-[sinA_/cosA]

=[1_/cosAsinA]-[sinA_/cosA]

=[1_/cosA][1_/sinA -sinA]

=[1_/cosA][(1-sin²A)_/sinA]

=[1_/cosA][cos²A_/sinA]

=[cosA_/sinA]

=cotA