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prove that 1/cos 290+1/root 3.sin 250=4/root 3

prove that 1/cos 290+1/root 3.sin 250=4/root 3

Grade:11

3 Answers

Sunil Raikwar
askIITians Faculty 45 Points
9 years ago
1/cos290+1/root3.sin250
=1/sin20 -1/root3.cos20
=root3cos20-sin20/root3.sin20.cos20
=4.(sin60co20-cos60sin20)/root3.2sin20cos20 [multiply and divide by 4]
=4sin40/root3.sin40= 4/root3
Thanks & Regards
Sunil Raikwar
askIITians Faculty
Jatin
26 Points
6 years ago
=1/sin20 -1/root3.cos20=root3cos20-sin20/root3.sin20.cos20=4.(sin60co20-cos60sin20)/root3.2sin20cos20 [multiply and divide by 4]=4sin40/root3.sin40= 4/root3
christo
15 Points
3 years ago
cos(290)=cos(270+20)=sin20
sin(250)=sin(270-20)= -cos20
therefore,1/cos290+1/root3.sin250=1/sin20-1/root3.cos20
=root3.cos20-sin20/root3.sin20*cos20 (by cross multiplying)
=2(root3/2cos20-1/2sin20)/(1/2*root3.2sin20cos20)    (2sin20.cos20=sin40)
=2(sin60.cos20-cos60.sin20)/(1/2*root3.sin40)    (sin60.cos20-cos60*sin20=sin40)
=4sin40/root3.sin40=4/roo3
 

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