(1+ sin A/cosec A - cot A) - (1- sin A/cosec A+ cot A) = 2(1 + cot A)
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Answer:
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Step-by-step explanation:
Solving LHS,
1+sin A / cosec A - cot A - 1- sin A/ cosec A+cot A
(1+sin A)(cosec A+ cot A) - (1-sin A)(cosec A- cot A) / cosec 2 A - cot2 A ......[(a+b)(a-b) =a2- b2]
cosec A + cot A + 1 + cos A - cosec A + cot A + 1 - cos A
2 + 2 cot A
2(1+ cot A) = RHS
2 answer
capturebus
capturebus
given: (1+ sinA)/(cosecA- cotA) - (1 - sinA)/(cosecA + cotA) = 2(1+cotA)
to find: prove the above equation.
now to solve such problems, we need to find first LHS and equate it with RHS.
Solving LHS first,
(1 + sinA/cosecA - cotA) - (1 - sinA/cosecA + cotA)
after converting all trigonometric ratios in terms of sin and cos, we get
(1+sinA)sinA / (1-cosA) - (1-sinA)sinA / (1+cosA)
Then we need to do cross multiplication,
{(1+sinA)(1+cosA)sinA - (1-sinA)(1-cosA)sinA}/ (1-cos²A)
Now 1-cos²A is sin²A, So replacing it
{(1+sinA)(1+cosA)sinA - (1-sinA)(1-cosA)sinA}/ (sin²A)
cancelling sinA from numerator and denominator, and multiply further,
{1+ sinA + cosA+ sinAcosA - (1- sinA-cosA+sinAcosA)}/ sinA
opening all brackets,
{1+ sinA + cosA+ sinAcosA - 1+ sinA+cosA-sinAcosA)}/ sinA
we get,
2sinA+2cosA/sinA
2(sinA+cosA)/sinA
2{1+ cotA} RHS
Answer:
