The value of 1 is of a) 2 2 sec - tan b) 2 2 sin - cos c) 2 sin - cos d) 2 2 cot cosec
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Answered by
1
(sinA+cscA)2+(cosA+secA)2
=sin2A+csc2A+2sinAcscA+cos2A+sec2A+2cosAsecA As[a²+b²+2ab=(a+b)²]
=sin2A+csc2A+2sinA×sinA1+cos2A+sec2A+2cosAcosA1 .
since secA=cosA1 and cscA=sinA1
=sin2A+csc2A+2+cos2A+sec2A+2
=(sin2A+cos2A)+csc2A+sec2A+4
=1+1+cot2A+1+tan2A+4 since csc2A=1+cot2A and sec2A=1+tan2A
=7+tan2A+cot2A
Answered by
1
sinA(1+tanA)+cosA(1+cotA)
= sinA(1+
cosA
sinA
)+cosA(1+
cosA
sinA
)
= (sinA+cosA)(
cosA
sinA
+
sinA
cosA
)
= (sinA+cosA)(
sinA+cosA
sin
2
A+cos
2
A
= secA+cosecA
Thus, 1 satisfies the given equation.
Step-by-step explanation:
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