Question

please answer fast......

Answer 1

tan(π cos∅) = cot( πsin∅)

we know ,
tan( π/2 - ∅) = cot∅
use this ,

cot( π/2 - πcos∅) = cot( πsin∅)

π/2 - πcos∅ = πsin∅

πsin∅ + πcos∅ = π/2

sin∅ + cos∅ = 1/2

√2{ 1/√2sin∅ + 1/√2cos∅} = 1/2

√2{ sin45°sin∅ + cos45°.cos∅} = 1/2

√2cos( ∅ - 45°) = 1/2

cos( ∅ - 45°) = 1/2√2

if we take -√2

-√2 { -1/√2 sin∅ - 1/√2cos∅ } = 1/2

-√2 { sin(-45°).sin∅ - cos( -45°).cos∅} =1/2


[ note :- cos(-∅) = cos∅ ]

-√2 cos{∅ +( -45°) } = 1/2

-√2 cos( ∅ -45°) = 1/2

cos( ∅ -45°) = -1/2√2

hence,

cos( ∅ - π/4) = ± 1/2√2

Answer 2

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