(Sin A + cosA) (tan A + cot A)=secA+ CosecA
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To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A= [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A= [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A= [cos A +sin A]/sin A cos A
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A= [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A= [cos A +sin A]/sin A cos A= (1/sin A) + (1/cos A)
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A= [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A= [cos A +sin A]/sin A cos A= (1/sin A) + (1/cos A)= cosec A + sec A = RHS.
To prove sin A(1+ tan A)+ cos A(1 + cot A) = sec A + cosec A.LHS = sin A(1+ tan A)+ cos A(1 + cot A)= sin A + sin^2 A/ cos A + cos A + cos^2 A/ sin A= sin A + cos A + [sin^3 A + cos^3 A]/sin A cos A=[ sin^2 A cos A + cos^2 A sin A + sin^3 A + cos^3 A]/sin A cos A= [ sin^2 A cos A +cos^3 A + cos^2 A sin A + sin^3 A]/sin A cos A= [cos A (sin^2 A + cos^2 A) + sin A (sin^2 A + cos^2 A)]/sin A cos A= [cos A +sin A]/sin A cos A= (1/sin A) + (1/cos A)= cosec A + sec A = RHS.Proved.