If cosa-cosb-m-and-cosa-sinb-n- show-that- m2-n2cos2b-n2-

L.H.S= (m^2+n^2)cos^2 b =(cosa/cosb)^2 +(cosa/sinb)^2 cos^2b =cos^2a/cos^2b +cos^2a/sin^2bcos^2b = (cos^2 a sin^2 b +cos^2a cos^2b)/cos^2b.sin^2bcos2^b = (c ...

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Byju's Answer

Standard X

Mathematics

Visualisation of Trigonometric Ratios Using a Unit Circle

If cosa/cosb=...

Question

If $\frac{c o s a}{c o s b} = m a n d \frac{c o s a}{s i n b} = n, s h o w t h a t : (m^{2} + n^{2}) c o s^{2} b = n^{2} .$

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Solution

L.H.S= $(m^{2} + n^{2}) c o s^{2} b$

= $(\frac{c o s a}{c o s b})^{2} + (\frac{c o s a}{s i n b})^{2} c o s^{2} b$

= $\frac{c o s^{2} a}{c o s^{2} b} + \frac{c o s^{2} a}{s i n^{2} b} c o s^{2} b$

= $\frac{(c o s^{2} a s i n^{2} b + c o s^{2} a c o s^{2} b)}{c o s^{2} b . s i n^{2} b} c o s 2^{b}$

= $\frac{(c o s^{2} a (s i n^{2} b + c o s^{2} b))}{s i n^{2} b}$

= $\frac{c o s^{2} a}{s i n^{2} b}$

= $n^{2}$ = R.H.S

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If cosacosb=m and cosasinb=n,show that:(m2+n2)cos2b=n2.

L.H.S= (m2+n2)cos2b =(cosacosb)2+(cosasinb)2cos2b =cos2acos2b+cos2asin2bcos2b = (cos2asin2b+cos2acos2b)cos2b.sin2bcos2b = (cos2a(sin2b+cos2b))sin2b = cos2asin2b =n2 = R.H.S

If $\frac{c o s a}{c o s b} = m a n d \frac{c o s a}{s i n b} = n, s h o w t h a t : (m^{2} + n^{2}) c o s^{2} b = n^{2} .$