Question

(1 +cotA-cosecA) (1 +tanA +secA)= 2

Answer 1

Answer

2

Step-by-step explanation:

Step 1: Multiplying each term within brackets we get,

=1+tanA+secA+cotA+cotAtanA+cotAsecA-cosecA-cosecAtanA-cosecAsecA

Step2: Expanding the terms cot, tan,sec,cosec like cos/sin, sin/cos, 1/cos, 1/sin respectively

= 1+ sinA/cosA + 1/cosA +cosA/sinA + (cosA/sinA)(sinA/cosA) + (cosA/sinA)(1/cosA) - 1/sinA - (1/sinA)(sinA/cosA) - (1/sinA)(1/cosA)

Step 3: Cancelling out the like terms we get

= 1+ sinA/cosA + cosA/sinA + 1 - (1/sinA)(1/cosA)

Step 4: Multiply numerator with sin A and cosA respectively to make it equal with the denominator. we get,

= (2sinAcosA + $sin^{2}A$ + $cos^{2}A$ - 1) / (sinA cosA)

we know the equation $sin^2 A + cos^2 A =1$

Hence the above equation becomes

= 2sinAcosA /sinAcosA

= 2

Hence solved