(sec∅ - tan∅)2(1 + sin∅)2 ÷ cos2∅ = ?
A. cos2∅
B. 1
C. cot2∅
D. -1
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\left( {\sec \phi - \tan \phi } \right)^2}{\left( {1 + \sin \phi } \right)^2} \div {\cos ^2}\phi \cr & = {\left( {\frac{1}{{\cos \phi }} - \frac{{\sin \phi }}{{\cos \phi }}} \right)^2}{\left( {1 + \sin \phi } \right)^2} \div {\cos ^2}\phi \cr & = {\left( {\frac{{1 - \sin \phi }}{{\cos \phi }}} \right)^2}{\left( {1 + \sin \phi } \right)^2} \div {\cos ^2}\phi \cr & = \frac{{{{\left( {1 - \sin \phi } \right)}^2}{{\left( {1 + \sin \phi } \right)}^2}}}{{{{\cos }^2}\phi }} \times \frac{1}{{{{\cos }^2}\phi }} \cr & = \frac{{{{\left( {1 - {{\sin }^2}\phi } \right)}^2}}}{{{{\cos }^4}\phi }} \cr & = \frac{{{{\cos }^4}\phi }}{{{{\cos }^4}\phi }} \cr & = 1 \cr} $$Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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