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Question

The expression (1−tanA+secA)(1−cotA+cosecA) has value.

A
1
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B
0
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C
+1
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D
+2
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Solution

The correct option is B +2
(1tanA+secA)(1cotA+cosecA)=(1sinAcosA+1cosA)(1cosAsinA+1sinA)

=(1+cosAsinA)(1+sinAcosA)sinAcosA

=(1+cosAsinA)(1(cosAsinA))sinAcosA

=1(cosAsinA)2sinAcosA

=1(sin2A+cos2A2sinAcosA)sinAcosA

=11+2sinAcosAsinAcosA

=+2

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