. prove that: (1 + cot θ − cosecθ)(1 + tan θ + sec θ) = 2
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Heya!
★ Thanks ★
see my answer step by step please!
given
( 1 + cot∅ - cosec ∅ ) ( 1 + tan∅ + sec∅ ) = 2
now
L.H.S.
( 1 + cot∅ - cosec∅ ) ( 1 + tan∅ + sec∅ )
= ( 1 + cos∅/sin∅ - 1/sin∅ ) ( 1 + sin∅/cos∅ + 1/cos∅ )
= ( cos∅ + sin∅ - 1/ sin∅ ) ( cos∅ + sin∅ + 1/ cos∅ )
= { ( cos∅ + sin∅ ) - 1 } { ( cos∅ + sin∅ ) + 1 } / sin∅.cos∅
= ( cos∅ + sin∅ )² - 1²/ sin∅.cos∅
= cos²∅ + sin²∅ + 2sin∅.cos∅ - 1 / sin∅.cos∅
= 1 + 2sin∅.cos∅ - 1 / sin∅.cos∅
= 2 sin∅.cos∅/sin∅.cos∅
= 2
★ proved ★
Wish you to have a sweat dreams ahead my Friend
===================================
★ Thanks ★
see my answer step by step please!
given
( 1 + cot∅ - cosec ∅ ) ( 1 + tan∅ + sec∅ ) = 2
now
L.H.S.
( 1 + cot∅ - cosec∅ ) ( 1 + tan∅ + sec∅ )
= ( 1 + cos∅/sin∅ - 1/sin∅ ) ( 1 + sin∅/cos∅ + 1/cos∅ )
= ( cos∅ + sin∅ - 1/ sin∅ ) ( cos∅ + sin∅ + 1/ cos∅ )
= { ( cos∅ + sin∅ ) - 1 } { ( cos∅ + sin∅ ) + 1 } / sin∅.cos∅
= ( cos∅ + sin∅ )² - 1²/ sin∅.cos∅
= cos²∅ + sin²∅ + 2sin∅.cos∅ - 1 / sin∅.cos∅
= 1 + 2sin∅.cos∅ - 1 / sin∅.cos∅
= 2 sin∅.cos∅/sin∅.cos∅
= 2
★ proved ★
Wish you to have a sweat dreams ahead my Friend
===================================
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