tan theta divided by 1 minus cot theta + cot theta divided by 1 minus tan theta is equal to 1 + tan theta + cot theta
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Step-by-step explanation:
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Step-by-step explanation:
let theta=x
(tanx/1-cotx)+(cotx/1-tanx)=1+tanx+cotx
LHS {tanx(-tanx)/(-tanx)(1-cotx)}+(cotx/1-tanx)
(-tan^2x/1-tanx)+(cotx/1-tanx)
(cotx-tan^2x)/(1-tanx)
(1/tanx-tan^2x)/1-tanx
1-tan^3x/tanx-tan^2x
(1-tanx)(1+tanx+tan^2x)/tanx(1-tanx)
1+tanx+tan^2x/tanx
cotx+1+tanx
1+tanx+cotx
hence proved
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