If tan theta=4/3, show that √(1-sin theta /1+sin theta ) = 1/3
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Tan theta = 4/ 3 = P / B
By pythagoras theorem,
H^2 = P^2 + B ^2
H ^2 = 16 + 9
H = √25 = 5 units.
Sin theta= P / H = 4 /5
√(1-sin theta /1+sin theta ) = 1/3
L. H. S. = √( 1 - 4/5) / ( 1 + 4 /5 )
=> √ ( 5 - 4) / ( 5 +4 )
=> √ 1 / 9
=> 1 / 3.
= R. H. S.
HENCE, PROVED.
By pythagoras theorem,
H^2 = P^2 + B ^2
H ^2 = 16 + 9
H = √25 = 5 units.
Sin theta= P / H = 4 /5
√(1-sin theta /1+sin theta ) = 1/3
L. H. S. = √( 1 - 4/5) / ( 1 + 4 /5 )
=> √ ( 5 - 4) / ( 5 +4 )
=> √ 1 / 9
=> 1 / 3.
= R. H. S.
HENCE, PROVED.
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