find the value of (1-tan ∅ +sec ∅)(1-cot ∅ +cosec ∅). (please give me the whole solution)
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Answer:
cotA−cosecA)(1+tanA+secA)=2
L.H.S.
=(1+cotA−cosecA)(1+tanA+secA)
=(1+
sinA
cosA
−
sinA
1
)(1+
cosA
sinA
+
cosA
1
)
=(
sinA
sinA+cosA−1
)(
cosA
cosA+sinA+1
)
=
sinA.cosA
(sinA+cosA)
2
−1
2
=
sinA.cosA
sin
2
A+cos
2
A+2sinA.cosA−1
=
sinA.cosA
1+2sinA.cosA−1
=
sinA.cosA
2sinA.cosA
=2=R.H.S.
Step-by-step explanation:
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