Answer:
Step-by-step explanation:
sin²β + sin²β×tan²β = tan²β
sin²β( 1 + tan²β ) = tan²β
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sin²β + cos²β = 1
[tex]\frac{sin^2\beta }{cos^2\beta }[/tex] + [tex]\frac{cos^2\beta }{cos^2\beta }[/tex] = [tex]\frac{1}{cos^2\beta }[/tex] ⇒ tan²β + 1 = sec²β ⇔ 1 + tan²β = sec²β
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1 + tan²β = [tex]\frac{1}{cos^2 \beta }[/tex]
L.H. = sin²β ( [tex]\frac{1}{cos^2 \beta }[/tex] ) = tan²β
R.H. = tan²β
