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sin A(1+tan A)+cos A(1+cot A)=sec A+cose...

`sin A(1+tan A)+cos A(1+cot A)=sec A+cosec A`

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sin A(1+tan A)+cos A(1+cot A)=sec A+cos ecA

7. (sin A+cos A)(cot A+tan A)=sec A+cosec A

(tan A+cot A)=(sec A*csc A)

(1+tan A)/(sin A)+(1+cot A)/(cos A)=2(sec A+cosec A)

(1+tan A+sec A)(1+cot A-cosec A)=

(tan ^ (3) A) / (1 + tan ^ (2) A) + (cot ^ (3) A) / (1 + cot ^ (2) A) = sec A cos ecA-2sin A cos A

Prove that (i) (tan A+ sin A)/(tan A- sin A)= (sec A+1)/(sec A-1) (ii) (cot A- cos A)/(cot A+ cos A)= ("cosec" A-1)/("cosec" A+1)

(tan A) / (1-cot A) + (cot A) / (1-tan A) = 1 + tan A + cot A = 1 + sec A cos ecA (1 + cos theta + sin theta) / (1 + cos theta-sin theta) = (1 + sin theta) / (cos theta)

(sin A)/(sec A+tan A-1)+(cos A)/(cos ecA+cot A-1)=1