Question

Find the value of (sinA + cosecA)2 + (cosA + secA)2 - (tan2A + cotA)​

Answer 1

$(sinA + cosecA) {}^{2} + (cosA + secA) {}^{2} - (tan2A + cotA) {}^{2}$

$= sin {}^{2} A + cosec {}^{2} A + 2sinA \times cosA + cos {}^{2} A + sec {}^{2} A + 2cosA \times secA - (tan {}^{2} A + cot {}^{2} A + 2tan \: A \times cosA)$

$= sin {}^{2} A + cosec {}^{2} A + 2+ cos {}^{2} A + sec {}^{2} A + 2 - tan {}^{2} A - cot {}^{2} A - 2$

$= (sin {}^{2} + cos {}^{2} ) + (tan {}^{2} A - cos {}^{2} A) + (cot {}^{2} A - cosec {}^{2} A) + 2 + 2 - 2$

$= 1 + 1 + 1 + 2$

$\huge\red{ \boxed{ \pink = 5}}$

$\huge\orange{\mathfrak{MARK\:BRAINLIEST}}$

Answer 2

Answer:

lsinA+cosecA)

2

+(cosA+secA)

2

−(tan2A+cotA)

2

= sin {}^{2} a + cosec {}^{2} a + 2sina \times cosa + cos {}^{2} a + sec {}^{2} a + 2cos \times sec - (tan {}^{2} a + cot {}^{2} a + 2tan \: a \times cosa)=sin

2

a+cosec

2

a+2sina×cosa+cos

2

a+sec

2

a+2cos×sec−(tan

2

a+cot

2

a+2tana×cosa)

= sin {}^{2} a + cosec {}^{2} a + 2+ cos {}^{2} a + sec {}^{2} a + 2 - tan {}^{2} a - cot {}^{2} a - 2=sin

2

a+cosec

2

a+2+cos

2

a+sec

2

a+2−tan

2

a−cot

2

a−2

= (sin {}^{2} + cos {}^{2} ) + (tan {}^{2} a - cos {}^{2} a) + (cot {}^{2} a - cosec {}^{2} a) + 2 + 2 - 2=(sin

2

+cos

2

)+(tan

2

a−cos

2

a)+(cot

2

a−cosec

2

a)+2+2−2

= 1 + 1 + 1 + 2=