Question

Evaluate: (sin85°/cos15°)^2 + (cos85°/sin15°)^2 - 2sin^2 (90°)( please say fast)​

Answer 1

Trigonometric values

To find: the value of $(\frac{sin85^{\circ}}{cos15^{\circ}})^{2}+(\frac{cos85^{\circ}}{sin15^{\circ}})^{2}-2\:sin^{2}90^{\circ}$

Solution:

• We know that, $sin(90^{\circ}-A)=cosA$
• and $cos(90^{\circ}-A)=sinA$

• Now, $(\frac{sin85^{\circ}}{cos15^{\circ}})^{2}+(\frac{cos85^{\circ}}{sin15^{\circ}})^{2}-2\:sin^{2}90^{\circ}$

• $=(\frac{sin(90^{\circ}-15^{\circ})}{cos15^{\circ}})^{2}+(\frac{cos(90^{\circ}-15^{\circ})}{sin15^{\circ}})^{2}-2\:(1)$

• $=(\frac{cos15^{\circ}}{cos15^{\circ}})^{2}+(\frac{sin15^{\circ}}{sin15^{\circ}})^{2}-2$

• $=1^{2}+1^{2}-2$

• $=1+1-2$

• $=0$

Answer: $(\frac{sin85^{\circ}}{cos15^{\circ}})^{2}+(\frac{cos85^{\circ}}{sin15^{\circ}})^{2}-2\:sin^{2}90^{\circ}=0$

Note:

• To solve this type of problems, remember that trigonometric formulæ:
• $sin(90^{\circ}-A)=cosA$
• $cos(90^{\circ}-A)=sinA$