1.

If sin 38° = x/y, then sec 38° - sin 52° is equal to1). \(\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}\)2). \(\frac{{{y^2}}}{{x\sqrt {{y^2} - {x^2}} }}\)3). \(\frac{{{x^2}}}{{y\sqrt {{x^2} - {y^2}} }}\)4). \(\frac{{{y^2}}}{{x\sqrt {{x^2} - {y^2}} }}\)

Answer»

cos 38° = √(1 – SIN238°) = √[1 – (X2/y2)] = √(y2 – x2)/y

sec 38° - sin 52°

= (1/cos 38°) - sin(90° - 38°)(? cos x = 1/sec x)

= (1/cos 38°) – cos 38°

= (1 – cos238°)/cos38°(? sin2x + cos2x = 1)

= sin238°/cos 38° 

$(\BEGIN{array}{L} = \;\frac{{\frac{{{x^2}}}{{{y^2}}}}}{{\frac{{\sqrt {{y^2} - {x^2}} }}{y}}}\; = \;\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}\\ \therefore {\rm{\;sec\;}}38^\circ {\rm{\;}} - {\rm{\;sin\;}}52^\circ \; = \;\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }} \end{array})$



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