Question

if sinA+cosA=√2 then evaluate:
tanA+cotA​

Answer 1

sin A + cos A=√2  

=(sin A + cos A)²=2  

=sin²A + cos²A + 2•sin A•cos A =2  

=1+2•sin A•cos A=2  

=2 sin A•cos A =1  

=sin A• cos A= 1/2  

tan A+ cot A= (sin A / cos A)+ (cos A/sin A)  

= {(sin²A+cos²A)/ (sin A•cos A)}  

={1/(1/2)}                                            { ∵ (sin²A+cos²A =1) &   ( sin A• cos A= 1/2)}

= 2  

∴ tan A+ cot A= 2

Hope its correct

Plz mark it as brainliest<3

Answer 2

sinA+cosA = √2

squaring both sides

(sinA + cosA)² = 2

1+2sinAcosA = 2

2sinAcosA = 1

sinAcosA = 1/2

Now

tanA + cotA

=1/sinAcosA

=1/(1/2)

=2