Question

√sec²A+√cosec²A=tanA+cotA

Answer 1

Answer:

taking L.H.S. to prove. Here is the explaination

Step-by-step explanation:

(1/√cos²A)+(1/√sin²A)

(1/cosA)+(1/sinA)

(sinA+cosA)/SinACosA

(SinA/CosA)+(cosA/sinA)

tanA+cotA

L.H.S=R.H.S

Answer 2

$\huge{\underline\mathfrak{\red{Answer : - }}}$

$\huge\underline{L \: H \: S}$

$\implies\sqrt{ \sec^2(A) + \cosec^2(A) }$

$\implies\sqrt{(1 + \tan^2(A))+(1+ \cos^2(A) }$

$\implies \sqrt{ \tan^2(A) + \cot2(A) +2}$

=$\implies \sqrt{ \tan^2(A)+ \cot^2(A) +2 \times 1}$

=$\sqrt{ \tan^2(A) + \cot2(A)+2( \tan(A) + \cot(A) }$

$\sqrt{( \tan(A) + \cot(A) )^2}$

$= \tan(A) + \cot(A)$

$= \huge\underline{ R \: H \: S}$

$\huge{\underline\mathfrak{Hence \: proved }}$