यदि ` sinA = 2/(sqrt(5))` तथा ` cosB = 1/(sqrt(10))` जहाँ A और B न्यून कोण है , तब `A +B` किसके बराबर है ?

Options

A. `135^(@)`
B. `90^(@)`
C. `75^(@)`
D. `60^(@)`

Answer

a

Explanation

` sin A = 2/(sqrt(5)), cos B = 1/(sqrt(10))`
` :. cos A = sqrt(1- sin^(2) A)= sqrt(1-4/5)= 1/(sqrt(5))`
` sin B = sqrt(1 - cos^(2) B)= sqrt(1-1/10)= 3/(sqrt(10))`
हमे ज्ञात है ,
` sin ( A+B) = sin a cos B + cos A sin B `
` = 2/sqrt(5) xx1/(sqrt(10))+1/(sqrt(5))xx3/(sqrt(10))`
` = 2/(sqrt(50))+ 3/(sqrt(50))= 5/(sqrt(50))=1/(sqrt(2))`
` :. sin ( A+B) = 1/(sqrt(2))`
` rArr sin ( A+ B) = sin (45^(@)) "व " sin 135^(@)`
` rArr A + B = 45^(@) " व " 135^(@)`