Question

If sinα- cosα=0, find tge value of sec(π/2-α)+cosec(π/2-α)

Answer 1

since

sinA - cosA=0,

then

sinA=cosA,

sinA/cosA =1,

tanA=1,

tanA=tan45°,

then

A=45°,


hence


sec(π/2-A) + cosec(π/2-A),

cosecA + secA,

cosec45° + sec45°,

√2 + √2,

2√2

Answer 2

sinα - cosα =0
sinα = cosα
α = π/4
sec(π/2 - π/4) + cosec(π/2 - π/4)
= sec(π/4) + cosec(π/4)
= √2 + √2
= 2√2