Question

If cos???? = 12/13, show that sin???? (1-tan????) = 35/156

Answer 1

we have to proved that sin????(1 - tan????) = 35/156

given, cos???? = 12/13

we know, cosine = base/hypotenuse

so, base = 12 and hypotenuse = 13

from Pythagoras theorem,

altitude = √(hypotenuse ² - base² )

= √(13² - 12²) = 5

now sin???? = altitude/hypotenuse = 5/13

and tan???? = altitude/base = 5/12

now sin????(1 - tan????) = 5/13 × (1 - 5/12)

= 5/13 × 7/12

= 35/156 [ hence proved ]

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