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(1 +tan^2 A)+(1+1÷tan^2 A)
=(1÷(sin^2 A - sin^4 A))
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Answer:
1+tan²A+(1+1/tan²A)
1+Sin²A/Cos²A+ (1+1/Sin²A/Cos²A)
1+Sin²A/Cos²A+(1+Cos²A/Sin²A)
Supposed that,
x=Sin²A
Sin²A=1-Cos²A
x=1-Cos²A
Cos²A=1-x
Then,
1+x/(1-x)+{1+(1-x)/x}
{(1-x)+x}/(1-x)+{x+(1-x)}/x
(1-x+x)/(1-x)+(x+1-x)/x
1/(1-x)+1/x
x+(1-x)/x(1-x)
(x+1-x)/x-x²
1/x-x²
Putting x as Sin²A
1/Sin²-Sin⁴A R.H.S
hence proved
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