Question

sec square theta + tan square theta =?​

Answer 1

Answer:

Answer:

tan^{2}\theta+cot^{2}\theta+2=sec^{2}\theta cosec^{2}\theta  

Step-by-step explanation:

LHS = tan^{2}\theta+cot^{2}\theta+2\\=(1+tan^{2}\theta)+(1+cot^{2}\theta)\\=sec^{2}\theta+cosec^{2}\theta

\* By Trigonometric identities:

i) 1+tan²A = sec²A

ii) 1+cot²A = cosec²A*/

=\frac{1}{cos^{2}\theta}+\frac{1}{sin^{2}\theta}\\=\frac{sin^{2}\theta+cos^{2}\theta}{cos^{2}\theta sin^{2}\theta}

=\frac{1}{cos^{2}\theta sin^{2}\theta}\\=\frac{1}{cos^{2}\theta}\times \frac{1}{sin^{2}\theta}\\=sec^{2}\theta cosec^{2}\theta \\=RHS