In prove of cos(x+y)=cosx.cosy-sinx.siny it is given that the line which makes angle x(degrees) has the coordinates 'cosx,sinx'(in 2nd quadrant).I understand that in circle of radius 1 which makes angle x in first quadrant will have cordinates cosx,sinx on the circle.and i think it should be -cosx,sinx for 2nd quadrant but in ncert book pg no.64 In prove of cos(x+y)=cosx.cosy-sinx.siny fig 3.14 it is given that in 2nd quadrant too the value is cosx,sinx.can you explain how? also can you explain sin 90+x=-cosx by diagram or prove geometrically?

CBSE Class 11-science Answered

In prove of cos(x+y)=cosx.cosy-sinx.siny

it is given that the line which makes angle x(degrees) has the coordinates "cosx,sinx"(in 2nd quadrant).I understand that in circle of radius 1 which makes angle x in first quadrant will have cordinates cosx,sinx on the circle.and i think it should be -cosx,sinx for 2nd quadrant but in ncert book pg no.64 In prove of cos(x+y)=cosx.cosy-sinx.siny fig 3.14 it is given that in 2nd quadrant too the value is cosx,sinx.can you explain how?

also can you explain sin 90+x=-cosx by diagram or prove geometrically?

Asked by Kamlesh Sahu | 07 May, 2014, 06:41: AM

Expert Answer

The proof in the NCERT book is correct . These points are basically parametric coordinates of a circle, whose values depend upon the arguments( x & y) of cosine and sine functions.

For second question

Consider,

$sin open parentheses 90 plus theta close parentheses equals sin A O P apostrophe equals fraction numerator M apostrophe P apostrophe over denominator O P apostrophe end fraction equals fraction numerator O M over denominator O P end fraction equals cos theta$

Answered by Avinash Soni | 07 May, 2014, 03:49: PM