Question

Sec⁴a-tan⁴a=1+2tna²a prove

Answer 1

${sec}^{2} a - {tan}^{2} a = 1$
now,
${sec}^{4} a - {tan}^{4} a \\ = ({{sec}^{2} a - {tan}^{2} a}) \times ({ {sec}^{2} a + {Tan}^{2} a}) \\ = 1 \times {sec}^{2} a + {tan}^{2} a \\ = 1 + {tan}^{2} a + {tan }^{2} \\ = 1 + 2 {tan}^{2} a$